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Journal of Mathematical Biology (2023) 87:24
https://doi.org/10.1007/s00285-023-01948-y
Mathematical Biology
Analysis of metapopulation models of the transmission
of SARS-CoV-2 in the United States
MyVan Vo1·Zhilan Feng1,2 ·John W. Glasser3·Kristie E. N. Clarke4·
Jefferson N. Jones3
Received: 5 October 2022 / Revised: 18 April 2023 / Accepted: 8 June 2023 /
Published online: 8 July 2023
This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may
apply 2023
Abstract
During the COVID-19 pandemic, renewal equation estimates of time-varying effec-
tive reproduction numbers were useful to policymakers in evaluating the need for
and impact of mitigation measures. Our objective here is to illustrate the utility
of mechanistic expressions for the basic and effective (or intrinsic and realized)
reproduction numbers, R0,RE, and related quantities derived from a Susceptible-
Exposed-Infectious-Removed (SEIR) model including features of COVID-19 that
might affect transmission of SARS-CoV-2, including asymptomatic, pre-symptomatic,
and symptomatic infections, with which people may be hospitalized. Expressions from
homogeneous host population models can be analyzed to determine the effort needed
to reduce REfrom R0to 1 and contributions of modeled mitigation measures. Our
model is stratified by age, 0–4, 5–9, …, 75+ years, and location, the 50 states plus
District of Columbia. Expressions from such heterogeneous host population models
include subpopulation reproduction numbers, contributions from the above-mentioned
infectious states, metapopulation numbers, subpopulation contributions, and equilib-
rium prevalence. While the population-immunity at which RE1 has captured the
popular imagination, the metapopulation RE≤1 could be attained in an infinite num-
ber of ways even if only one intervention (e.g., vaccination) were capable of reducing
RE.However, gradients of expressions derived from heterogeneous host population
models,∇RE, can be evaluated to identify optimal allocations of limited resources
among subpopulations. We illustrate the utility of such analytical results by simulating
BJohn W. Glasser
jglasser@cdc.gov
1Department of Mathematics, Purdue University, West Lafayette, USA
2Division of Mathematical Sciences, NSF, Alexandria, USA
3Coronavirus and Other Respiratory Viruses Division, National Center for Immunization and
Respiratory Diseases, CDC, 1600 Clifton Road NE, Atlanta, GA 30333, USA
4Center for Surveillance, Epidemiology, and Laboratory Services, CDC, Atlanta, USA
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