The Mathematics of Serocatalytic Models with applications to public health data

Abstract Serocatalytic models are powerful tools which can be used to infer historical infection patterns from age-structured serological surveys. These surveys are especially useful when disease surveillance is limited and have an important role to play in providing a ground truth gauge of infection burden. In this tutorial, we consider a wide range of serocatalytic models to generate epidemiological insights. With mathematical analysis, we explore the properties and intuition behind these models and include applications to real data for a range of pathogens and epidemiological scenarios. We also include practical steps and code in R and Stan for interested learners to build experience with this modelling framework. Our work highlights the usefulness of serocatalytic models and shows that accounting for the epidemiological context is crucial when using these models to understand infectious disease epidemiology. Competing Interest Statement The authors have declared no competing interest. Funding Statement JC is supported by the Moh Family Foundation on an Oxford-Moh Family Foundation Global Health Scholarship. SB is supported by the Clarendon Scholarship, St. Edmund Hall College, and NERC DTP [grant number NE/S007474/1], University of Oxford. This work was also supported by the UK NIHR Health Protection Research Unit (HPRU) in Emerging and Zoonotic Infections, a partnership between UKHSA, University of Oxford, University of Liverpool and Liverpool School of Tropical Medicine (grant number NIHR200907 supporting C.A.D.). NT and ZC were supported by the TRACE-LAC project (Enhancing Tools for Response, Analytics and Control of Epidemics in Latin America and the Caribbean) [grant number: 109848-002], funded by the International Development Research Center (IDRC). Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes Footnotes ↵* indicates joint first authors. everlyn.kamau{at}ucsf.edu junjie.chen{at}stats.ox.ac.uk sumali.bajaj{at}seh.ox.ac.uk ex-ntorres{at}javeriana.edu.co richard.creswell{at}unimelb.edu.au jpavlich{at}javeriana.edu.co christl.donnelly{at}stats.ox.ac.uk zulma.cucunuba{at}javeriana.edu.co ben.lambert{at}stats.ox.ac.uk Funding statement updated; author affiliations updated; Data Availability All data analyzed are available at https://github.com/ekamau/serocatalytic_models.