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Analysis of metapopulation models of the transmission of SARS-CoV-2 in the United States

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During the COVID-19 pandemic, renewal equation estimates of time-varying effective 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, [Formula: see text] 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 [Formula: see text] from [Formula: see text] to 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 equilibrium prevalence. While the population-immunity at which [Formula: see text] has captured the popular imagination, the metapopulation [Formula: see text] could be attained in an infinite number of ways even if only one intervention (e.g., vaccination) were capable of reducing [Formula: see text] However, gradients of expressions derived from heterogeneous host population models,[Formula: see text] can be evaluated to identify optimal allocations of limited resources among subpopulations. We illustrate the utility of such analytical results by simulating two hypothetical vaccination strategies, one uniform and other indicated by [Formula: see text] as well as the actual program estimated from one of the CDC's nationwide seroprevalence surveys conducted from mid-summer 2020 through the end of 2021.
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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 RE1 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
123
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Background Case-based surveillance of pediatric COVID-19 cases underestimates the prevalence of SARS-CoV-2 infections among children and adolescents. Our objectives were to estimate monthly SARS-CoV-2 antibody seroprevalence and calculate ratios of SARS-CoV-2 infections to reported COVID-19 cases among children and adolescents in 8 U.S. states. Methods Using data from the Nationwide Commercial Laboratory Seroprevalence Survey, we estimated monthly SARS-CoV-2 antibody seroprevalence among children aged 0-17 years from August 2020 through May 2021. We calculated and compared cumulative incidence of SARS-CoV-2 infection extrapolated from population-standardized seroprevalence of antibodies to SARS-CoV-2, cumulative COVID-19 case reports since March 2020, and infection: case ratios among persons of all ages and children aged 0-17 years for each state. Results Of 41,583 residual serum specimens tested, children aged 0-4, 5-11 and 12-17 years accounted for 1,619 (3.9%), 10,507 (25.3%) and 29,457 (70.8%), respectively. Median SARS-CoV-2 antibody seroprevalence among children increased from 8% (range, 6% to 20%) in August 2020 to 37% (range, 26% to 44%) in May 2021. Estimated ratios of SARS-CoV-2 infections to reported COVID-19 cases in May 2021 ranged by state from 4.7-8.9 among children and adolescents to 2.2-3.9 for all ages combined. Conclusions Through May 2021 in selected states, the majority of children with serum specimens included in serosurveys did not have evidence of prior SARS-CoV-2 infection. Case-based surveillance underestimated the number of children infected with SARS-CoV-2 more than among all ages. Continued monitoring of pediatric SARS-CoV-2 antibody seroprevalence should inform prevention and vaccination strategies.
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Importance People who have been infected with or vaccinated against SARS-CoV-2 have reduced risk of subsequent infection, but the proportion of people in the US with SARS-CoV-2 antibodies from infection or vaccination is uncertain. Objective To estimate trends in SARS-CoV-2 seroprevalence related to infection and vaccination in the US population. Design, Setting, and Participants In a repeated cross-sectional study conducted each month during July 2020 through May 2021, 17 blood collection organizations with blood donations from all 50 US states; Washington, DC; and Puerto Rico were organized into 66 study-specific regions, representing a catchment of 74% of the US population. For each study region, specimens from a median of approximately 2000 blood donors were selected and tested each month; a total of 1 594 363 specimens were initially selected and tested. The final date of blood donation collection was May 31, 2021. Exposure Calendar time. Main Outcomes and Measures Proportion of persons with detectable SARS-CoV-2 spike and nucleocapsid antibodies. Seroprevalence was weighted for demographic differences between the blood donor sample and general population. Infection-induced seroprevalence was defined as the prevalence of the population with both spike and nucleocapsid antibodies. Combined infection- and vaccination-induced seroprevalence was defined as the prevalence of the population with spike antibodies. The seroprevalence estimates were compared with cumulative COVID-19 case report incidence rates. Results Among 1 443 519 specimens included, 733 052 (50.8%) were from women, 174 842 (12.1%) were from persons aged 16 to 29 years, 292 258 (20.2%) were from persons aged 65 years and older, 36 654 (2.5%) were from non-Hispanic Black persons, and 88 773 (6.1%) were from Hispanic persons. The overall infection-induced SARS-CoV-2 seroprevalence estimate increased from 3.5% (95% CI, 3.2%-3.8%) in July 2020 to 20.2% (95% CI, 19.9%-20.6%) in May 2021; the combined infection- and vaccination-induced seroprevalence estimate in May 2021 was 83.3% (95% CI, 82.9%-83.7%). By May 2021, 2.1 SARS-CoV-2 infections (95% CI, 2.0-2.1) per reported COVID-19 case were estimated to have occurred. Conclusions and Relevance Based on a sample of blood donations in the US from July 2020 through May 2021, vaccine- and infection-induced SARS-CoV-2 seroprevalence increased over time and varied by age, race and ethnicity, and geographic region. Despite weighting to adjust for demographic differences, these findings from a national sample of blood donors may not be representative of the entire US population.
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Background A rubella vaccine was licensed in China in 1993 and added to the Expanded Programme on Immunization in 2008, but a national cross-sectional serological survey during 2014 indicates that many adolescents remain susceptible. Maternal infections during the first trimester often cause miscarriages, stillbirths, and, among livebirths, congenital rubella syndrome. We aimed to evaluate possible supplemental immunisation activities (SIAs) to accelerate elimination of rubella and congenital rubella syndrome. Methods We analysed residual samples from the national serological survey done in 2014, data from monthly rubella surveillance reports from 2005 and 2016, and additional publications through a systematic review. Using an age-structured population model with provincial strata, we calculated the reproduction numbers and evaluated the gradient of the metapopulation effective reproduction number with respect to potential supplemental immunisation rates. We corroborated these analytical results and estimated times-to-elimination by simulating SIAs among adolescents (ages 10–19 years) and young adults (ages 20–29 years) using a model with regional strata. We estimated the incidence of rubella and burden of congenital rubella syndrome by simulating transmission in a relatively small population lacking only spatial structure. Findings By 2014, childhood immunisation had reduced rubella's reproduction number from 7·6 to 1·2 and SIAs among adolescents were the optimal elimination strategy. We found that less than 10% of rubella infections were reported; that although some women with symptomatic first-trimester infections might have elected to terminate their pregnancies, 700 children could have been born with congenital rubella syndrome during 2014; and that timely SIAs would avert outbreaks that, as susceptible adolescents reached reproductive age, could greatly increase the burden of this syndrome. Interpretation Our findings suggest that SIAs among adolescents would most effectively reduce congenital rubella syndrome as well as eliminate rubella, owing both to fewer infections in the immunised population and absence of infections that those immunised would otherwise have caused. Metapopulation models with realistic mixing are uniquely capable of assessing such indirect effects. Funding WHO and National Science Foundation.