Optimal intervention strategies for a new pandemic: The case of Covid-19*

Optimal intervention strategies for a new pandemic: The case of Covid-19* | medRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-P4HH5NV'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search Optimal intervention strategies for a new pandemic: The case of Covid-19 * View ORCID Profile Steinar Holden , View ORCID Profile Gunnar Rø , View ORCID Profile Ingrid Hjort doi: https://doi.org/10.1101/2024.12.04.24318460 Steinar Holden 1 University of Oslo Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Steinar Holden For correspondence: steinar.holden{at}econ.uio.no Gunnar Rø 2 Norwegian Institute of Public Health 3 Handelshoyskolen BI Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Gunnar Rø Ingrid Hjort 1 University of Oslo Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Ingrid Hjort Abstract Full Text Info/History Metrics Supplementary material Data/Code Preview PDF Abstract We present an age-stratified SEIR-type model of the Norwegian population, which is extended to include the effects of broad types of Non-Pharmaceutical Interventions (NPIs) like general lockdown-policies, contact tracing and quarantine and border control. The model can be used to explore the spread of a new virus with given virulence and transmissibility, and to assess the main costs of the disease and the NPIs in terms of lost health and welfare as well as economic losses. We define the optimal strategy as the intervention policy which minimizes the total costs from the pandemic, including health, economic and other welfare effects. We find that the optimal policy typically is a “bang-bang-strategy”, where costly interventions are either so strict that the pandemic is suppressed to a low level, or they are not used at all. Strict interventions may be used to stop the disease at the herd immunity level (i.e prevent pandemic overshoot), while mitigation policies aimed at merely slowing the spread of the pandemic are not optimal in our baseline simulations. We explore how the optimal strategy depends on the properties of the virus, healthcare capacity, intervention costs, population behavior and other relevant variables. These results are informative for decisions regarding costly investments and interventions. In addition, we explore the consequences of policy errors and delays, providing guidance for decision making in the uncertain early stages of a new pandemic. 1 Introduction If countries are facing a new dangerous pandemic, how should the authorities respond? Close the borders to avoid the disease coming to the country? Implement strict lock-down legislation to suppress the pandemic? In the wake of the Covid-19 pandemic, a large amount of research have explored the effects of Non-Pharmaceutical Interventions (NPIs), generally finding that NPIs can be effective in containing the pandemic, see e.g. ( Deb et al., 2020 ; Flaxman et al., 2020 ; Haug et al., 2020 ; Levelu & Sandkamp, 2023 ; Liu et al., 2021 ; Turner et al., 2021 ). There is also clear indication, at least among rich economies, that countries which chose early implementation of strict interventions during the Covid-19 pandemic fared better than countries with later or no strict interventions, at least in the first part of the pandemic, see e.g. ( Caselli et al., 2020 ; Demirguc-Kunt et al., 2020 ). However, in spite of the valuable experiences and research from the Covid-19 pandemic, there are no clear guidelines or broad agreement on how and under which circumstances interventions should be used under a possible new dangerous pandemic. The lack of clear guidelines and agreement partly reflects that the evolution of a pandemic is highly complex, determined by the characteristics of the virus, structural characteristics of the population and the country, like population density, health, mobility patterns, climate etc., the behavioral response of the inhabitants as well as the use of NPIs. Moreover, even if the determinants of the pandemic had been well understood, policy decisions would still depend on the evaluation of the disparate consequences and costs of the disease, in terms of health, welfare, and economy, including distributional effects. In many countries, Covid-19 policies were highly controversial, and often correlated with other political lines of conflict, see e.g. ( Gonzalez-Eiras & Niepelt, 2022 ). If a new pandemic emerges, the controversies and lack of agreement on policies may impair the handling of the disease, making policy selection and implementation more difficult. To explore the policy dilemmas, a number of scholars have developed models integrating epidemic and economic mechanisms, often referred to as epi-econ or integrated models, see e.g. ( Acemoglu et al., 2021 ; Alvarez et al., 2021 ; Atkeson, 2020 ; Boppart et al., 2022 ; Boucekkine et al., 2024 ; Brotherhood et al., 2024 ; Eichenbaum et al., 2021 ; Farboodi et al., 2021 ; Kaplan et al., 2020 ; Piguillem & Shi, 2022 ; Pollinger, 2023 ). These models can be used to analyze health and societal consequences of the disease and interventions, as well as exploring tradeoffs between various consequences. When calibrated with realistic parameter values, such models can also be used for actual policy analysis and decisions, see e.g. ( Boppart et al., 2024 ; Goenka et al., 2024 ; Haw et al., 2022 ; Lee et al., 2022 ; Rubinstein et al., 2022 ; Wagner et al., 2021 ). We present an age-stratified SEIR-type model of the Norwegian population, extended to include the effects of broad types of government interventions like general lockdown-policies, contact tracing and quarantine and border control. The model can be used to explore the spread of a new virus with given virulence and transmissibility, and to assess the main costs of the disease and interventions in terms of lost health and welfare as well as economic losses. We define the optimal strategy as the intervention policy which minimizes the total costs from the pandemic, including health, economic and other welfare effects. We then explore how the optimal strategy depends on the properties of the virus, the capacity of the health sector, the costs of interventions, the behavior of the population and other relevant factors. We also explore the consequences of policy errors and delays, which may inform decision making during the uncertain early stages of a new pandemic. We show that the optimal policy is typically a “bang-bang-strategy”, implying that costly interventions are either so strict that the pandemic is suppressed to a very low level, or they are not used at all. Strict interventions may be used to keep the pandemic at a minimum, or to stop the disease when the herd immunity level is reached, to prevent additional epidemic spread (pandemic “overshoot”, cf. e.g. ( Britton & Leskelä, 2023 ; Di Lauro et al., 2021 )). In contrast, intermediate alternatives like mitigation or “flatten-the-curve” policies where interventions are used to slow the evolution of the pandemic are not optimal in our baseline simulations. Intuitively, a bang-bang solution implies that the authorities choose the lesser among two evils, either the pandemic or costly interventions. In contrast, a mitigation strategy will involve both health and other costs of the pandemic, as well as economic and welfare costs of the interventions. We find that mitigation policies may be optimal with longer time to effective vaccination and much higher valuation of health effects of overburdened hospitals than under our baseline assumptions. The guidelines for optimal policy are intuitive in the sense that strict interventions are used if the virus is sufficiently dangerous. However, the guidelines also have the counterintuitive feature that large health costs will mainly be apparent in situations where strict interventions are not used. Thus, if the disease leads to considerable health loss, it might be difficult to explain that the losses are not sufficiently severe to justify the use of costly interventions. Likewise, it might also be difficult to justify strict interventions when the pandemic is suppressed, implying that very few people are harmed by the disease. The purpose of the analysis is three-fold. First, the model can be used as a laboratory to explore the health and societal consequences and tradeoffs of various intervention policies. Crucially, the optimal policy depends critically on the characteristics of the virus and the effect of interventions, and there is no general optimal policy. Second, when the model is calibrated to a specific country and virus, it can be used as a tool when selecting and communicating the optimal policy. Furthermore, the model can be used to explore how the gains or costs of specific policies or interventions, like travel restrictions and increased hospital capacity, depend on the overall intervention strategy. We show that the gains and costs of specific interventions depend crucially on the chosen overall strategy, making it vital to analyze the consequences along the chosen policy path. Such analyses may also be useful for decisions on how to prepare for a possible future pandemic. Third, by exploring the effects of policy errors and delays, the model can be used to analyze the gains and losses of delaying interventions while learning more about the properties of the virus. Our numerical results are clearly virus- and country-specific, as they are based on a model of Covid-19 in Norway. The literature indicates that the effects of interventions have varied across countries and over time, see e.g. ( Deb et al., 2020 ; Levelu & Sandkamp, 2023 ). However, we believe that the basic modeling framework is sufficiently flexible so that it can be used to explore policy alternatives and derive policy guidelines also for other countries and other pathogens. For a pandemic with similarities to SARS-CoV-2, it might be sufficient to review the calibration of the model to the new pathogen. For a pathogen with more fundamental differences in key characteristics, it would be necessary to change parts of the model. In our view, other countries could also benefit from developing similar models, tailored and calibrated to reflect their specific structural and demographic characteristics. 2 The model We consider the arrival of a new variant of SARS-CoV-2, which is described by two dimensions: an initial reproduction number R ∈ [1.2, 3], and effective severity ES ∈ [1, 20], mapped on the existing Norwegian population. Effective severity ES = 1 corresponds approximately to the early Omicron wave in Norway, with a high degree of immunity in the population from both vaccines and previous infections. The probabilities of hospitalization and death increase linearly with effective severity, implying that ES = 15 approximately corresponds to the original Wuhan variant in a naïve population. We use a metapopulation SEIR-type model with nine age groups to explore the epidemic trajectories. The model belongs to a family of metapopulation models used for Covid-19 analysis at the Norwegian Institute of Public Health (NIPH) ( Chan et al., 2024 ; Engebretsen et al., 2023 ), similar to models used in e.g. ( Davies et al., 2020 ; IHME COVID-19 Forecasting Team, 2021 ). The model was extended with costs by an expert group giving advice to the Norwegian authorities during the Covid-19 pandemic ( Holden et al., 2022 ), and we build on this work. 1 2.1 Interventions and individual responses in a pandemic The spread of the virus is affected by both government interventions like testing, contact tracing and quarantine (TTIQ) and non-pharmaceutical interventions (NPIs) aimed at general contact reduction, and voluntary social distancing, where individuals choose to limit their social interactions to lower the risk of infection for themselves and others, see e.g. ( Atkeson, 2020 ; Eichenbaum et al., 2021 ; Farboodi et al., 2021 ; Traulsen et al., 2023 ; Yan et al., 2021 ). Based on experiences from the early Covid-19 pandemic in Norway, Engebretsen et al. (2023) found that the lockdown in March/April 2020 led to a substantial and statistically significant reduction in the reproduction number R , with a point estimate of 85%. The regional estimates varied from a reduction of 69% to 93%. Based on this, we assume that the maximum reduction in the contact rate, from maximum government interventions, including a system of Testing-Tracing-Isolation-Quarantine (TTIQ), and maximum voluntary social distancing, is a reduction in R by 90%. To analyze the optimal level of government interventions, it is important to explore the relationship between interventions and voluntary social distancing. From a theoretical level, one would expect that many of the effects overlap, but also that voluntary social distancing may complement government interventions. For example, if agents avoid stores to reduce their personal risk of infection, there will be little additional effect from a legal restriction closing stores. However, containment policies may also restrain individuals who disregard the health risk and prevent behavior which follows from strong social norms or uncoordinated action in spite of considerable health risk. Many studies seek to empirically distinguish the effects of government interventions from those of voluntary social distancing, see e.g. ( Allcott et al., 2020 ; Goolsbee & Syverson, 2021 ; Sheridan et al., 2020 ). Findings vary widely, and in a review of the literature, ( Meunier & Bricongne, 2021 ) find that the effects attributed to lockdown measures range from 12% to 60%. This wide variation may be due to differences in the use of interventions and the extent of voluntary social distancing, as well as challenges in accurately separating these effects. We are not aware of empirical evidence that can be used to identify the effect of NPIs without any voluntary social distancing. It seems plausible that most of the effects will overlap, but also that intense voluntary social distancing may have a substantial additional effect beyond the effect of NPIs. Specifically, we assume that if government interventions, TTIQ and NPIs, are used without voluntary social distancing, the maximum possible reduction in the contact rate is 80%. As TTIQ is cheap relative to more stringent lockdown measures, particularly when infection rates are low, we assume that if the authorities use measures to contain the pandemic, they will start with TTIQ, for then to proceed with other NPIs. As a robustness, we show in Supplementary Appendix that the main qualitative results hold also without the possibility of TTIQ. As a rough estimate based on the Norwegian experiences during the pandemic, we assume that full implementation of TTIQ leads to a reduction in the spread of the disease that corresponds to a reduction in the contact rate of 20%. Turner et al. (2021) finds a small but statistically significant effect on R across OECD countries, while Fetzer and Graeber (2021) documents a fairly strong effect from TTIQ in Britain. 2.2 Government interventions In the model, the use of government interventions is measured by an index on the unit interval, G ∈ [0, 1]. The first quarter up to G = 0.25 represents TTIQ, which gives a contact reduction by 20%, while further interventions are assumed to be NPIs, which are generic contact-reducing measures that lower the virus’s effective reproduction rate. The idea is to capture the overall effect of various interventions, such as workplace closures, school guidelines, cancellation of public events, public transport closures, restrictions on gathering sizes. We do not distinguish between different types of interventions. In general, the authorities should use interventions that lead to a large reduction in transmissions relative to the costs associated with lost output and welfare. However, while there is strong empirical evidence that interventions work, the evidence for the effect of specific interventions is more uncertain and often conflicting, as illustrated by the discussion of the literature in Turner et al. (2021) . Thus, our model can be used to analyze the optimal level of intervention in general, but not which specific interventions to use. Information and guidelines from the authorities may also have a crucial role in reducing fear and helping the population to behave in ways that reduce the health risk, but such policies are not explicitly included in our framework. However, as the model can be used to explore the consequences of different types of individual behaviour, it can used for designing guidelines for population behaviour during a pandemic. 2.3 Voluntary social distancing Various approaches to voluntary social distancing have been used in the literature, from empirically based relationships based on mobility measures ( Piguillem & Shi, 2022 ) or the death rate from the virus ( Turner et al., 2021 ), to assumptions of full information rational expectations ( Boppart et al., 2024 ). We assume that individuals compare the welfare costs of staying at home over a period of 60 days with the expected health costs from the risk of infection associated with a normal life during this period. A fairly long period of 60 days is based on an assumption that individuals realize that social distancing will have to be continued for a long time to prevent infection. The average welfare costs of voluntarily staying at home is set at 285 NOK per day (around 28 USD), based on a Swedish choice experiment conducted in mid-April 2020 ( Andersson et al., 2022 ). As the experiment shows considerable individual variation, costs are assumed to be uniformly distributed from 0 to 570 NOK per day (see Supplementary Appendix , section C for details). The expected health costs from continuing with normal life are calculated on the basis of the contemporaneous probability of infection, multiplied by age-specific loss of QALY from infection. We use a logistic transformation to ensure a gradual response from the relative utility of social distancing to the actual choice taken by the individual. This transformation captures that individuals may abstain from actions involving high risk, yet they may take some risk in other situations. Our approach has the advantage that the choice of voluntary social distancing is based on the individual health risk in terms of probability of being infected and expected health loss conditional on being infected, relative to the individual welfare loss from social distancing. However, it also involves a strong assumption regarding the information and decision capacity in the population. In Supplementary Appendix section C, we show that the main results are robust to variations in the extent of voluntary social distancing. 2.4 Contact rate The overall reduction in the contact rate for age group i from interventions G and voluntary distancing V i is: This formulation is chosen to capture that government NPIs and voluntary distancing V i ∈ [0, 1] to a large extent will overlap, but they will also complement each other. The formulation ensures that , ie. a 90% reduction in the contact rate, for G = V i = 1, while if only government interventions or only voluntary social distancing are used ( G = 1; V i = 0) or ( G = 0; V i = 1). We assume that the effect of G and V i on the contact rate is constant over time. An empirical analysis of a panel of 152 countries by Goldstein et al. (2021) finds evidence of considerably “lockdown fatigue”, where the effectiveness of NPIs diminishes over time. The reduced effect over time may partly result from increased non-compliance, implying a reduction in associated costs as well. However, Goldstein et al. (2021) also find diminishing health benefits from a reduction in de facto mobility, suggesting that the efficiency of NPIs, in terms of effect relative to costs, may deteriorate over time. Our assumption of constant effect and constant costs of interventions implies that measures are reinforced if their effect weakens, and that authorities find ways to maintain their effectiveness relative to costs. This assumption should be evaluated carefully if the authorities consider implementing a strict and lengthy suppression strategy. 2.5 The cost of interventions The government interventions imposed in Norway in March 2020, which we have used to calibrate the maximum reduction of the contact rate, led to a sharp fall in GDP of more than 10%. However, as society and workplaces adapted to the restrictions and fiscal support was implemented, the economic impact was less severe when similar interventions were imposed the following winter. The reduction in GDP, measured by the output gap calculated by Statistics Norway, was 4.6% of mainland GDP, corresponding to 12.7 bnNOK (billion Norwegian kroner) per month. The revised intervention index developed by Bjørnland et al. (2024) confirms that the interventions during winter 2021 were as stringent as those implemented in March/April 2020. When including the tax financing costs, ie. the efficiency loss from increased taxes due to the government’s substantial financial expenditures, estimated by ( Holden et al., 2022 ) at 2 bnNOK per month, the total economic cost amounts to about 15 bnNOK per month. The expert group Holden et al. (2022) found no evidence of learning loss at kindergartens, schools and universities during the Covid-19 pandemic in Norway, suggesting that the guidelines used after the initial lockdown in March/April 2020 worked well. We include learning loss for students who are sick or in quarantine, but not as part of the intervention costs. Since our measure of economic costs is based on the reduction in GDP, it does not account for changes in the composition of activities across sectors and firms and within organizations. In cases where regular activities and planned investments were replaced by efforts to manage and adapt to the pandemic and interventions, this approach will underestimate the loss of output and welfare that would have been generated by those regular activities. Contact-reducing measures also result in welfare losses due to reduced social activity. These losses are calibrated using a choice experiment by Andersson et al. (2022) , which we also use for calibrating the costs of voluntary social distancing. In the experiment, Swedish participants indicated they would require a compensation of 2,000 SEK (about 200 USD or 2,000 NOK) per week for a 4-week stay-at-home policy with limited outside activity. This translates to an average welfare loss of 285 NOK per person per day. Assuming this loss applies for the maximum reduction in the contact rate of 90%, the total welfare cost for Norway’s population of 5.4 mn is approximately 47 bnNOK per month. This brings the total intervention cost to 62 bnNOK per month, about 22% of mainland GDP in 2021, the base year for our calculations. To make the intervention costs a continuous function of the intervention level, we define an auxiliary quadratic function: Note that K (1) = 62, equal to the costs from maximum interventions ( G = V = 1), while K (0.5) = 24.5, implying a convex cost function where 50% of the maximal reduction in the contact rate costs 40% of the total costs for the maximum reduction (as 24.5 / 62 ≈ 0.4). The overall cost from contact reduction for age group i is: 2 Here, f i is the fraction of the population in age group i . The total cost from contact reduction is then given by: We assume that each change in intervention level ΔG is associated with a cost, up to a maximum cost of 3bnNOK for large changes in G , see Supplementary Appendix . The extra cost represents information, decision and implementation cost of changing interventions. Such costs prevent solutions with frequently changing G . The costs of TTIQ are calculated separately and added to the cost of contact reduction. These costs include administrative expenses and economic and welfare effects for individuals in isolation or quarantine. The costs are assumed to be proportional to the extent of TTIQ, see Supplementary Appendix . 2.6 The cost of the disease The disease may also involve large health losses in terms of symptomatic infections, hospitalizations, treatment in the Intensive Care Unit (ICU), post acute sequela and deaths. We measure the health loss in terms of lost Quality Adjusted Life Years (QALYs), calibrated to the estimates of QALYs from Covid-19 in Holden et al. (2022) , see Supplementary Appendix . To express the health loss in monetary values we assume a value of 1.4 mnNOK per QALY. This value is taken from the recommended Value of a Statistical Life Year (VSLY) in 2021 for cost-benefit analysis in Norway. 1.4 mnNOK is about 5 times the value of household consumption per capita in Norway in 2021. For comparison, Glover et al. (2023) set VSLY to 6.25 times annual per capita consumption in the US in 2019, and Hall et al. (2020) use 6 times annual per capita consumption. We assume a 20% mortality rate for patients with Covid-19 in the ICU at normal capacity, based on the study by Vieillard-Baron et al. (2022) . Based on evidence from Castagna et al. (2022) , we assume a linear effect of an overburdened ICU, where an increase in the number of patients equal to 1% of the capacity leads to an increase in mortality by 0.7% of the mortality at full capacity, up to a maximum of 75% mortality. We assume that this increase applies uniformly to Covid-19 and non-Covid-19 patients due to triage considerations. The average death in the ICU is assumed to involve a loss of 10.4 QALYs, based on the assumption that ICU mortality follows a similar exponential increase with age as overall Covid-19 mortality in Norway, weighted by the age distribution of those who have received ICU treatment for Covid-19 in Norway. 3 Each admission to the ICU when it is operating above capacity by X percent is thus associated with an additional loss of 10.4(0.2 + 0.7% X ) life-years (up to 75% mortality). 2.7 Vaccine A crucial issue when handling a pandemic is the availability of an effective vaccine. In view of the rapid development of vaccines during the Covid-19 pandemic, it seems reasonable to assume that a vaccine will also be developed for a new virus. In our baseline scenario, we assume that an effective vaccine or treatment will become available after 9 months, effectively eliminating further infections. This is a crucial assumption which clearly depends on the new pathogen. In the formal model we treat the timing of the vaccine as certain. However, in Supplementary Appendix we discuss conditions when the main results are likely to hold also in the case where the timing of the vaccine is a stochastic variable, but the authorities can make an estimate of the expected timing of the vaccine. As a pragmatic way of simulating the effects when the vaccine arrives, we add a cool-down period of 150 days with R eff = 0.7 after vaccination. This ensures that we include the full health cost of the people infected before vaccination. In line with most of the literature, we assume that individuals who have been infected by the virus will have immunity to re-infection for the time span until vaccination. Thus, individuals who have recovered cannot be re-infected. We assume that it is not possible to eliminate the virus by use of strict intervention policy, including TTIQ. During the pandemic, several countries for a long time succeed in keeping the infection at essentially zero, benefiting from more natural borders, like New Zealand, or stricter regimes, like China. However, Norway is an open country with considerable cross-border movement making such polices more difficult. 2.8 Optimal Strategy The epi-econ literature typically explores the optimal policy defined as the policy which maximizes welfare or minimizes costs in the society, see e.g. ( Alvarez et al., 2021 ; Eichenbaum et al., 2021 ; Farboodi et al., 2021 ; Piguillem & Shi, 2022 ). Other objective functions used in the literature include minimizing a measure of economic loss subject to keeping infections within the capacity of the hospitals, see e.g. ( Haw et al., 2022 ), minimizing total incidence of the disease subject to bounds on the intensity and/or total interventions, see e.g. ( Bliman & Duprez, 2021 ; Britton & Leskelä, 2023 ), or minimizing peak prevalence of the disease, see e.g. ( Greene & Sontag, 2022 ). We define the optimal strategy as the time-varying level of interventions imposed by the government, G ( t ), that minimises the total costs of the pandemic and interventions, L T in equation [5]. The optimization is over government interventions G , including contact tracing (TTIQ) and contact reduction (NPIs). Other policies, such as hospital capacity and border controls, are treated as fixed in the baseline scenario, but are further explored in Figure 7 . As the model is deterministic, there is no uncertainty about the evolution of the pandemic given the path of interventions G ( t ). By using the infectious disease model, M, each strategy G ( t ) gives a specific disease outcome-space, s ( t ), and an associated amount of voluntary social distancing per age group, V i ( t ). The vector θ denotes the set of all the parameters in the model. where K T is the total costs from contact reduction given by equation [4]. L ΔG is the cost of changing the intervention level, L Q is the health loss from Covid-19 disease, L HC is the health loss from hospitals operating above capacity, L SICK is the economic and welfare cost when infected, and L T T IQ represents the cost of the TTIQ program including both the administrative costs of running the program and the economic and welfare costs associated with quarantine and isolation. We parameterise G ( t ) as a piecewise constant function and numerically find the optimal values of these constants. This is a challenging optimisation due to the large number of parameters, non-convexity of the cost function, the need for derivative free optimisation and the comparatively slow run-time of the model, see Supplementary Appendix for details. We assume that the pandemic starts with a small number of infected individuals (900), and that there is a limited inflow of infections from abroad (1 per day in the baseline scenario). 3 Results In this section we explore the characteristics of the optimal strategy, and how it depends on key assumptions and parameter values. The optimal strategy falls into one of three broad categories. In a suppression strategy, interventions are used to push the effective reproduction rate close to or below unity, thus keeping infections at a very low level. In a cut-overshoot strategy, infections are allowed to grow unconstrained until the herd immunity level is reached, and at this point strict interventions are used to stop the pandemic and prevent excess sickness. Finally, for no-interventions, the health loss from the pandemic is not sufficient to warrant the use of costly contact-reducing interventions. Thus, the optimal policy is of the “bang-bang” type, where interventions are either at suppression level or not used. The criteria for categorizing and labeling strategies are further discussed in Supplementary Appendix . Our findings have clear similarities to the results in Piguillem and Shi (2022) , which explore the optimal policy in a model that is fairly similar to ours, calibrated to the Italian economy. In the case where testing is not possible, Piguillem and Shi (2022) find that three possible optimal policies arise: suppression, mitigation and no-intervention. The cut-overshoot strategy is consistent with findings in Britton and Leskelä (2023) , Di Lauro et al. (2021) , and Nguyen et al. (2023) . Broadly, the results are also consistent with findings in Boppart et al. (2024) . Figure 1.A shows how the optimal strategy depends on the initial reproduction number and the effective severity of the virus. For a virus with a low reproduction number, a suppression strategy (red area) is optimal because the disease can be controlled at low costs through testing and tracing. Note that a suppression strategy does not necessarily require strict contact reduction; it is sufficient that interventions keep infections at a low level by ensuring that the effective reproduction number is near one. For a virus with higher reproduction number, suppression requires stricter and thus more costly interventions, which can only be justified for a more severe virus. For a virus with high reproduction number, but low severity, the lowest costs are associated with no-interventions (green area). Finally, for high transmissibility and moderate severity, the cut-overshoot strategy is optimal (blue area). In this case the health costs cannot justify the welfare costs associated with a full suppression strategy, yet it is worthwhile to close down the society for a limited period to avoid many infections beyond the herd immunity level. Download figure Open in new tab Figure 1: The baseline scenario for different values of R and ES . (A) Optimal strategy. (B) Average intervention level. (C) The number of total infections with an optimal strategy compared to a strategy with no interventions. (D) The total cost, LT , in bnNOK. Figure 1.B shows the associated average intervention level until vaccination. Under a suppression strategy, the required level of intervention is stricter for higher R, while for low R close to one, suppression can be achieved by use of TTIQ only. For the cut-overshoot strategies, the effect of R on the average level of intervention is much smaller. Figure 1.C shows the fraction of infections relative to the number of infections without interventions. Suppression reduces the number of infections to a minimal level, but not zero. The cut-overshoot strategy reduces the number of infections by 25% to 50%, implying a relative fraction of infections between 0.5 and 0.76. Finally, figure 1.D displays the total costs under the optimal strategy. For low R , the infection can be kept down at low cost by use of TTIQ. For higher R , suppression requires costly contact-reducing interventions, and we observe that it is the combination of high R and high effective severity, ES , which raises costs the most. A striking feature is the discontinuity of the optimal strategy at the border between different strategies. At the border, a minor change in the properties of the virus can lead to a sharp change in the optimal policy, changing between no-intervention, cut-overshoot and full suppression. This finding is also emphasized in some of the previous contributions in the literature ( Caulkins et al., 2021 ; Piguillem & Shi, 2022 ). This feature reflects the existence of Skiba points ( Caulkins et al., 2021 ), where two sharply different strategies yield the same cost level, making the decision maker indifferent between the strategies. An implication of this feature, emphasized in Piguillem and Shi (2022) , is that similar countries may optimally choose entirely different strategies if they are on opposite sides of the border between different strategies. The discontinuity of the optimal strategy from full suppression to no-interventions or vice versa reflects that intermediate policies are less attractive because they involve large costs from both interventions and the pandemic. Figure 2 shows that the different strategies lead to highly different evolution of the infection rates for the 380 ( R, ES )-combinations under the baseline scenario. Download figure Open in new tab Figure 2: Incidence of infections sorted into labeled policy groups in the baseline scenario. Each line represents an ( R, ES )-combination, where R ∈ [1.2, 3] and ES ∈ [1, 20] give 19*20=380 combinations. 3.1 Intervention timelines and categories of strategies Figure 3 illustrates the different types of strategies by displaying 16 examples of optimal intervention timelines in a 4-by-4 matrix of ( R, ES )-combinations. The top rows with high severity ( ES = 18 and ES = 12) show suppression strategies, where interventions are stricter (higher G ) for higher R . Note that interventions are relaxed in the last weeks or months before vaccination, to save intervention costs by allowing the effective R to be above 1. For ES = 6 (third row from top), suppression is chosen for R = 1.4 and R = 1.8, while the cut-overshoot strategy with a sharp lockdown when the pandemic peaks is chosen for higher initial R-values. Observe that in the cut-overshoot strategies, TTIQ is used fully ( G = 0.25) after the lockdown. This may reflect that the strict lockdown is stopped some days before herd immunity is reached, implying that some interventions, typically TTIQ, is used to keep infection down afterwards. The bottom row shows that for the lowest severity level ES = 1, suppression mostly consisting of TTIQ is employed for R = 1.4, as this is sufficient to control the disease for R = 1.4, while no-interventions are used for higher values of R . Download figure Open in new tab Figure 3: The baseline scenario: Optimal G ( t )-trajectories over time for a subset of initial reproduction numbers R = {1.4, 1.8, 2.2, 3} (columns) and severity levels ES = {1, 6, 12, 18} (rows). 3.2 How costs depend on the intervention level To illustrate key parts of the model, Figure 4 shows how the different types of costs depend on the level of interventions G ( t ) for R = 1.8 and three different severity levels. ‘Contact Reduction’ is the economic and welfare costs from government interventions and voluntary social distancing. This line is downward-sloping for G < 0.25, because the increase in G in this interval reflects more resources for TTIQ, which reduces the disease and thus also leads to less voluntary social distancing, ie. lower costs from contact reduction. For G > 0.25, contact-reducing NPIs are imposed, and the costs of contact reduction increases sharply. ‘Direct QALY Loss’ shows the health loss from the disease, L Q in eq [5], which is decreasing in G because interventions reduce the number of infections. ‘Hospital Capacity’, L HC , is the excess health costs associated with higher mortality rates in overloaded hospitals. From the right figure, we see that these costs may be large for high severity combined with a low level of interventions G ( t ). ‘TTIQ’, which is L T T IQ in eq [5], are increasing up till G = 0.25, when TTIQ is used to the full extent. Further increase in G represents contact-reducing NPIs which reduces the number of infections and thus also reduces the costs from TTIQ. ‘Production Loss Illness’, L SICK , is the economic and welfare cost for the infected, which is only a small part of the total costs. Download figure Open in new tab Figure 4: The baseline scenario: The figure shows how the various types of costs depend on the intervention level G ( t ), assuming that the intervention level is kept constant over time, for R = 1.8 and severity levels ES = {1, 7, 15}. 3.3 The monetary value of a QALY We now examine how the optimal strategy depends on key assumptions in the baseline scenario. Figure 5.A and 5.B show the effects of adjusting the monetary value of health loss. With a 50% reduction in the value of QALYs, suppression strategies cannot be justified for high R values, leading to cut-overshoot strategies even for severe variants. (For comparison, the solid black line indicates the optimal strategy boundary in the baseline scenario as displayed in Figure 1.A .) In contrast, with a 50% increase suppression strategies dominate, even for fairly low severity. Note that the strategy choice depends on the relative valuation of health effects to intervention costs. Thus, a 100% increase in the intervention costs would essentially have the same effect as a 50% reduction in the QALY value, as the change in the ratio of health to intervention costs is the same. Note also that if the health consequences, such as severe long term effects, are worse than we assume, this would be equivalent to a higher value of a QALY. Download figure Open in new tab Figure 5: Optimal strategy as a function of R and ES for the scenarios: (A) a 50% reduction in the value of a QALY, (B) a 50% increase in the value of a QALY, (C) 18 months to effective vaccination, and (D) 18 months to effective vaccination and 50% increased value of a QALY. The solid line marks the strategy boundary in the baseline scenario. 3.4 Time to vaccination Figure 5.C shows that if the time until effective vaccination is increased to 18 months, the suppression strategy becomes much less attractive, because the costly interventions must be in place for longer time. Thus, the cut-overshoot strategy is optimal even for severe viruses, and suppression is only used for low R. However, figure 5.D shows that with increased monetary valuation of QALYs, suppression is optimal for high severity levels even if the duration to vaccination is 18 months. 3.5 Mitigation (“flatten-the-curve”) A noteworthy feature of our results is that mitigation policies - flatten-the-curve - where interventions are used to slow the spread to prevent an overburdened health sector on the way to herd immunity, are not optimal under our baseline assumptions. For high severity levels, suppression is better than mitigation because the reduction in health costs is greater than the additional intervention costs. For lower severity levels, cut-overshoot is better than mitigation, because the reduction in intervention costs outweighs the additional costs from overburdened hospitals. To explore the robustness of this result, we modify the assumptions to make a mitigation strategy more attractive. To raise the costs of a suppression strategy, we increase the time to vaccination to 3 years. The result is that Cut-overshoot dominates except for low R or low severity, cf. Figure 6.A . However, if we in addition increase the costs of a QALY by a factor of 2 and the costs of overburdened hospitals by a factor of 4, mitigation is optimal for a small share of ( R, ES )-combinations, cf purple area in 6.C. If the costs of overburdened hospitals is increased by a factor of 10, mitigation is optimal for a larger proportion of ( R, ES )-combinations, cf 6.D. Download figure Open in new tab Figure 6: Optimal strategy as a function of R and ES in scenarios with 3 years until effective vaccination. (A) all other assumptions are as in baseline. (B) double the value of a QALY. (C) double the value of a QALY and 4 × the cost of overcapacity in hospitals. (D) double the value of a QALY and 10 × the cost of overcapacity. 3.6 Effects of policy changes In this subsection, we examine how changes in other policy areas, such as border control and hospital capacity, affect the optimal intervention strategy and its associated costs. Such analyses can provide valuable insights for investment and intervention decisions during a pandemic or in preparation for future pandemics. The left panels of Figure 7 show the optimal policy after the policy change and the right panels display the associated effect on total costs. Download figure Open in new tab Figure 7: Optimal strategy as a function of R and ES for different policy scenarios (left) and associated costs (right) compared to baseline, with red indicating costs and blue indicating savings. Scenario: (A-B) a generic reduction in transmission, (C-D) increased import of infections, (E-F) expanded ICU capacity and (G-H) vaccination with a weak vaccine. Figure 7.A and 7.B show the effect of a generic reduction in the transmission of the virus of 10%, eg. from increased indoor ventilation at schools or public buildings, or the use of face masks. The left panel shows that this change makes the suppression strategy more attractive, implying that it is used for a larger set of ( R, ES )-combinations. The right panel illustrates why, by displaying how the reduction in cost depends on the virus characteristics. Reduced transmission of the virus involves a considerable cost reduction for suppression strategies as it reduces the need for costly interventions, in particular for low to moderate initial reproduction numbers. However, if the no-interventions strategy is optimal, there is little or close to no gain from a generic reduction in transmission. This illustrates that the gain from specific interventions depends crucially on the chosen strategy, and thus must be evaluated along the chosen policy path. Figure 7.C and 7.D show the effect of an increased daily inflow of 210 infected individuals from abroad, corresponding to about 40 per million people. This makes the suppression strategy less attractive, as stricter interventions must be used to keep the effective reproduction number sufficiently below unity to compensate for the imported infections. This may lead to a considerable increase in overall costs for virus variants with high severity (right panel). In contrast, imported infections have little effect on total costs if no interventions are used, as imports in this case will have limited effect on the number of overall infections. This illustrates that strict border controls might be a useful tool as part of a suppression strategy, but it is less meaningful without other contact-reducing interventions. This is in sharp contrast to the policy choice in several countries, including the US., during parts of the pandemic, when strict border restrictions were combined with limited use of domestic interventions. Figure 7.E and 7.F show the effects of an 29% increase in the ICU capacity, from 350 to 450 beds. Increased ICU capacity reduces the costs associated with an overburdened health system, thus reducing the health costs of letting the epidemic grow without constraints. This involves considerable reduction in overall costs for virus variants with high transmissibility and severity, for which the cut-overshoot strategy is used. In contrast, for virus variant where the suppression strategy is optimal, the epidemic is constrained, leading to no burden on ICU capacity, hence the gain is negligible. Information about the gains from increased ICU capacity is useful for decisions on costly investments to increase capacity. Figure 7.G and 7.H present the effects of the use of a vaccine with some, but weak effect, eg. based on old strains, which mitigates susceptibility and health loss from infection. This involves a considerable reduction in health costs for a virus variant with high initial reproduction number and moderate to high severity. 3.7 Distributional Effects We have defined the optimal strategy as the strategy which gives the lowest total costs for the population as a whole. However, as Covid-19 involves much higher health risk for older and more vulnerable individuals, the choice of strategy has important distributional effects. In our model, we can explore the effects across age groups, but not differences across groups depending on socio-economic or health-related characteristics. To illustrate the distributional effects across age groups, Figure 8.A and B show the costs per age group and per person in the age group for a ( R, ES )-combination where the total costs are about the same under suppression and cut-overshoot. Under our assumptions, there is little variation in costs across age groups under a suppression strategy, except that the few infections involve higher health risk for older individuals. Under a cut-overshoot strategy, the higher infection rates impose greater health costs and greater costs from voluntary social distancing for the old, whereas the younger age groups benefit from the absence of costly contact-reducing interventions. Download figure Open in new tab Figure 8: Costs per age group (panel A) and costs per person in each age group (panel B) in baseline with an initial reproduction number of 2.5 and a severity of 11. The overall costs of the suppression and cut-overshoot strategies are approximately equal, while the no-interventions strategy has a higher total cost. The unequal distribution of health costs in a cut-overshoot strategy implies that the majority of the population —specifically those under 50 years of age — would prefer this approach to a suppression strategy. Due to the continuity of the cost function, this would still hold true even with slightly higher severity, where total costs would be lowest under the suppression strategy. Given the structure of our model, it is difficult to explore other types of distributional consequences. It is well known that the costs of both interventions and the disease are unevenly distributed across the population, with vulnerable groups — such as children, the elderly, minorities, immigrants, and low-income individuals — bearing a disproportionate burden ( Berchet et al., 2023 ; Kocks et al., 2024 ; National Institute of Public Health, 2021 ). In addition, workers in certain sectors and occupations are more exposed to infections, and firms and workers in these areas also face greater economic costs from interventions ( Altmejd et al., 2023 ). 3.8 Uncertainty At the early stage of a new pandemic, there may be large uncertainty about the transmissibility and severity of the virus variant, making it difficult to decide whether strict interventions should be imposed. Figure 9.A shows the additional costs from making an incorrect policy choice for two weeks, ie. no-interventions if suppression is optimal, or suppression if the optimal strategy is no-interventions or cut-overshoot. After two weeks, the optimal strategy under full information is used. We observe that the costs of using an incorrect strategy are increasing in R . For an incorrect suppression strategy, this reflects that the intervention costs are larger for higher R . For an incorrect no-interventions strategy, the increased costs reflect that the disease spreads more rapidly for higher R , increasing the cost of a subsequent suppression. Download figure Open in new tab Figure 9: Top: The increase in costs from using an incorrect strategy for two weeks. Bottom: The optimal strategy after two weeks with exogenous policy: no-interventions (left); suppression (right). The costs associated with an incorrect strategy are useful for assessing the value of early information about the characteristics of the virus. This may inform decisions on preparation for and managing a pandemic. An interesting feature of Figure 9.A is that the additional costs of an incorrect strategy are higher in the lower part of the ( R, ES )-diagram, indicating that the costs of an incorrect suppression strategy are higher than incorrectly delaying the intervention. The asymmetry may be relevant for decision making if there is uncertainty about the severity of the virus. Figures 9.B and 9.C show the optimal strategy when the authorities reoptimize after a two week period of exogenous policy; no-interventions (B) or suppression (C). For borderline cases it may be optimal to continue the existing policy after two weeks, even if it was inoptimal at the beginning, but otherwise the best is to pursue the strategy that was optimal at the beginning. If authorities change strategy during a pandemic, it may lead to large adjustment costs for households and organizations, undermine confidence and support for the policies, and may involve substantial political costs. These costs are likely to depend on how the change is implemented, the explanations provided, and the level of public trust in the authorities. Such costs are not included in our analyses, but they should be taken into account when applying the model in practice. If the characteristics of a virus are unknown, but there is enough information to establish a meaningful probability distribution for its transmissibility and severity, the model can be used to calculate the expected costs of different strategies, allowing authorities to choose the one with the lowest expected cost. 4 Discussion The aim of the model and analysis is to develop a general and flexible quantitative framework which can be used to explore how the cost-minimizing strategy for a possible new dangerous pathogen depends on the transmissibility and severity of the pathogen. The model is calibrated based on experiences from the Covid-19 pandemic in Norway and other countries. We believe the model represents a plausible and realistic framework, yet there is clearly large uncertainty about key parameters and modeling assumptions. In this section we will discuss some of the most important ones. In our analysis, the optimal strategy is defined as the strategy that minimizes the adverse effects on health, economy and welfare. Note that we do not assume that the authorities have a well-defined loss function over the various types of adverse effects from the pandemic and interventions. In reality, there may be substantial uncertainty and disagreement on the valuation of the different types of effects, and the authorities must also take into account political concerns and procedural matters, like the legal basis for imposing interventions. There might also be concerns and ethical dilemmas if restrictions and costs are imposed on some groups to reduce the risk for others ( Kollepara et al., 2024 ). However, we believe our analysis provides useful information for decision making, even if the authorities do not subscribe to a specific loss function. It is useful to explore which policy minimizes the total adverse effects from the pandemic and interventions, and how this policy depends on key parameters like virus characteristics, the efficiency and costs of NPIs, and the valuation of various types of consequences, even if the authorities also take other considerations into account. The costs and effects of government interventions will depend on the specific interventions used, how they are implemented, and how they are respected by the population. The model is calibrated for Norway, which is a rich country with a well-educated population, generally good housing conditions, good access to telecommunications, low inequality and a high level of trust. These conditions are likely to be helpful in containing the pandemic ( Helliwell et al., 2021 ). Fotiou and Lagerborg (2021) argue that countries with prior experience with similar viruses have implemented smarter containment measures, achieving a more efficient balance between the costs and benefits of interventions. There may be gains from using differentiated restrictions, imposing stricter interventions for the young than for the old ( Brotherhood et al., 2024 ) or more protective measures for the more vulnerable elderly population ( Acemoglu et al., 2021 ). The long term effects of infection are uncertain, and we would have little evidence to inform us if a new pathogen arrives. Possible severe long-term effects of infection would increase the health costs of the pandemic, as in the analysis above with a higher monetary value of a QALY. As shown, this would make suppression a more attractive strategy. However, there is also uncertainty about long term effects of interventions, including mental effects for children and teenagers. A crucial assumption in the analysis is that each individual can only be infected once, i.e. that infection involves immunity when the patient recovers, which lasts until effective vaccination is possible. This is a simple and transparent way of capturing that for most viruses, subsequent infections, if they occur, are considerably less serious. Hansen et al. (2021) found an 80% protection against reinfection after the first surge of Covid-19. However, after Omicron variants emerged, reinfections have increased substantially, even if severity usually is lower than for first infections ( Wei et al., 2024 ). The model can be extended to allow for subsequent infections ( Bjørnstad et al., 2020 ). Reinfections will add costs to the cases where the optimal strategy is either no-interventions or cut-overshoot, as herd immunity will only be temporary. The effects of adding reinfections to the model would therefore need to be studied in detail. For reasons of transparency and tractability, we have neglected seasonal effects and regional differences in the spread of the virus. Such effects could be incorporated in the model, and this might be important for practical use in a real pandemic. For example, regional representation could make it possible to explore whether regional differences in infection rates might warrant different intervention policies across regions. We have assumed that it is not possible to eliminate the virus. This is motivated by the situation of a country like Norway, with considerable trade and mobility with neighboring countries. However, if the disease burden is high, elimination of the virus is likely to be a good strategy if it is feasible, as argued by among others ( Baker et al., 2023 ; Oliu-Barton et al., 2021 ), and analyzed by ( Piguillem & Shi, 2022 ; Pollinger, 2023 ). An interesting finding is that cut-overshoot strategies may be optimal for a fairly large set of parameter values. Here, the pandemic is allowed to grow towards the herd immunity level, when a strict temporary lock-down is imposed. Afterwards, infections can be kept down by limited interventions, typically TTIQ. In principle, a cut-overshoot strategy should be feasible as long as the authorities have sufficient information to be able to determine when herd immunity is reached. However, there may also be important practical problems. For a severe virus, the population may respond by reducing social contacts to avoid being infected, thus delaying the spread of the virus and prolonging the time until herd immunity is reached ( Atkeson, 2020 ). A cut-overshoot strategy may also involve important challenges in terms of communication and trust in the population. In the analysis, we assume that the decision maker has full information about the relevant mechanisms and parameter values, including the characteristics of the virus and the effect of interventions. This is important to ensure tractability and a clear analysis, but it is also unrealistic. If the model is used for decision making during a real pandemic, the authorities must carefully evaluate the robustness of the policy conclusions against possible errors and limitations of the model. Some type of errors will have limited effect. For example, limited errors in the assessment of the severity of the virus or the time duration until effective vaccination will also lead to limited changes in the total costs of the chosen strategy. Other types of errors may be more crucial. For example, a lengthy suppression policy may result in a costly and difficult situation if “lockdown fatigue” impairs the effect of the intervention, causing a spread of the virus. A lengthy suppression policy may also be problematic if the expected vaccine is delayed or is less efficient than expected. Some aspects of uncertainty can be analyzed with minor extensions of the model, as illustrated by the analysis above of the costs of an incorrect strategy for two weeks. Other types of uncertainty would require further modifications of the model and analysis and is left for future research. 5 Concluding remarks In this paper we present a calibrated SEIR-model for Norway, extended to capture the main health, welfare and economic effects from Covid-19 and government interventions. The model is intended as a tool for preparing for potential future pandemics and guiding policy decisions if a new pandemic occurs. With appropriate adjustments to fit the specific pandemic at hand, the model can be used to explore the consequences of different policies and to identify and communicate the optimal strategy. The model can also be used to evaluate the benefits of specific measures, such as stricter border controls, increased ICU capacity, or generic interventions that reduce transmission. We show that the optimal intervention strategy, defined as the strategy which minimizes the total costs from the pandemic and interventions, typically is a “bang-bang-solution”, where the government either imposes strict interventions to suppress the disease, or let the disease spread without costly interventions. Typically, the optimal strategy falls into one of three categories, suppression, cut-overshoot or no interventions. Mitigation policies may be optimal in scenarios with longer time to effective vaccination and much higher costs of overburdened hospitals than under our baseline assumptions. Our analysis shows that a pandemic will involve several features that may complicate policy making over time. A key problem is the complexity of the interaction between the pandemic, government interventions and individual behaviour, as well as the disparate consequences in terms of health, welfare and economy. The complexity and disparate consequences are likely to lead to conflicting views and strong controversies regarding how the pandemic should be handled. With conflicting views and strong controversies it may often be a good idea to seek compromise and choose a middle-of-the-road policy. However, our analysis indicates that this may be costly when handling a pandemic. As the optimal strategy is either strict suppression or no costly intervention (alternatively “cut-overshoot”, implying first no interventions and then strict suppression), attempts to find a compromise may lead to inferior mitigation policies with high costs from both interventions and the pandemic. Pursuing a consistent policy — be it suppression or no-interventions — may also be politically difficult because the adverse effects from the policy are more readily apparent than the benefits. During suppression, strict interventions will constrain and frustrate individuals, with adverse effects for welfare and economy, while the concern for the virus may be weak as very few are sick. In Norway, the total mortality rate fell during the pandemic in 2020, as the reduction in mortality from other causes due to the interventions exceeded the mortality from Covid-19. In contrast, with no interventions, the health loss from the pandemic and overburdened hospitals will lead to fear and critique, while the benefit from the absence of restrictions may carry less weight. This may in particular be problematic for a virus variant which is close to the borderline between two optimal strategies, implying that there is little difference in total societal costs from two sharply different policies. In this situation, relatively small differences in the evaluation of various types of costs may lead to sharply different policy conclusions. Likewise, relatively small changes in the information about the virus characteristics may also lead to a sharp change in the optimal strategy. Another complicating feature is that the adverse effects from the pandemic and the interventions will be unequally distributed, with some age groups being more hurt by the pandemic, while other groups (with some overlap) will be more hurt by the interventions. One implication is that the policy that minimizes the total costs for the population may differ from the policy that benefits the majority of the population. Data Availability All computer code used for processing and data analysis is available at: https://github.com/folkehelseinstituttet/covid19_economic_evaluation https://github.com/folkehelseinstituttet/covid19_economic_evaluation Footnotes ↵ ‡ gunnaroyvindisaksson.ro{at}fhi.no , Norwegian Institute of Public Health. ↵ § ingrid.hjort{at}bi.no , BI Norwegian Business school. # We thank seminar participants at the National Institute of Public Health and the Workshop for Pandemic Preparedness in Stockholm for valuable feedback, and members of the expert group behind ( Holden et al., 2022 ) for excellent collaboration. Holden has received financial support from the Norwegian Research Council, grant no 324615. Data, method and software availability. The method is described further in Supplementary Appendix . 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