Sensitivity of endemic behaviour of Covid-19 under a multi-dose vaccination regime, to various biological parameters and control variables

For an infectious disease such as Covid-19, we present a new four-stage vaccination model (un-vaccinated, dose 1+2, booster, repeated boosters), which examines the impact of vaccination coverage, vaccination rate, generation interval, control reproduction number, vaccine efficacies, and rates of waning immunity, upon the dynamics of infection. We derive a single equation that allows computation of equilibrium prevalence and incidence of infection, given knowledge about these parameter and variable values. Based upon a 20 compartment model, we develop a numerical simulation of the associated differential equations. The model is not a forecasting or even predictive one, given the uncertainty about several biological parameter values. Rather, it is intended to aid qualitative understanding of how equilibrium levels of infection may be impacted upon, by the parameters of the system. We examine one at a time sensitivity analysis around a base case scenario. The key finding which should be of interest to policy makers, is that while factors such as improved vaccine efficacy, increased vaccination rates, lower waning rates, and more stringent non-pharmaceutical interventions might be thought to improve equilibrium levels of infection, this might only be done to good effect, if vaccination coverage on a recurrent basis, is sufficiently high.