Mathematical models of COVID-19 vaccination in high-income countries: A systematic review

Objectives Since COVID–19 first emerged in 2019, mathematical models have been developed to predict transmission and provide insight into disease control strategies. A key research need now is for models to inform long–term vaccination policy. We aimed to review the variety of existing modelling methods, in order to identify gaps in the literature and highlight areas for future model development. Study design This study was a systematic review. Methods We searched PubMed, Embase and Scopus from 1 January 2019 to 6 February 2023 for peer-reviewed, English-language articles describing age–structured, dynamic, mathematical models of COVID–19 transmission and vaccination in high–income countries that include waning immunity or reinfection. We extracted details of the structure, features and approach of each model and combined them in a narrative synthesis. Results Of the 1109 articles screened, 47 were included. Most studies used deterministic, compartmental models set in Europe or North America that simulated a time horizon of 3.5 years or less. Common outcomes included cases, hospital utilisation and deaths. Only nine models included long COVID, costs, life–years or quality of life–related measures. Two studies explored the potential impact of new variants beyond Omicron. Conclusions This review demonstrates a need for long–term models that focus on outcome measures such as quality–adjusted life years, the population–level effects of long COVID and the cost–effectiveness of future policies — all of which are essential considerations in the planning of long–term vaccination strategies. ### Competing Interest Statement HC reports grants from NIHR (HPRU BSE) and grants from NIHR (personal fellowship) during the conduct of the study; and in the last 5 years: GSK, grant as PI, payment made to institution, work separate from the submitted work; NIHR, grants as co-applicant, payment made to institution, work separate from the submitted work; Pfizer, grant as co-applicant, payment made to institution, work separate from the submitted work; UK Research and Innovation, grant as co-applicant, payment made to institution, work separate from the submitted work; Elizabeth Blackwell Institute University of Bristol, grant as PI, payment made to institution, work separate from the submitted work; ECDC, grant as co-PI, payment made to institution, work separate from the submitted work; and Member of the Scientific Advisory Panel, Meningitis Research Foundation. ### Clinical Protocols ### Funding Statement This study was funded by the NIHR Health Protection Research Unit in Behavioural Science and Evaluation at University of Bristol, in partnership with UK Health Security Agency (UKHSA) [grant number NIHR200877]. The views expressed are those of the author and not necessarily those of the NIHR, the Department of Health and Social Care, or UKHSA. The funding body was not involved in the design of the study, the interpretation of the model output or in the writing of the manuscript. ### 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 All data produced in the present study are available upon reasonable request to the authors