Mathematical assessment of the roles of age heterogeneity and vaccination on the dynamics and control of SARS-CoV-2

The COVID-19 pandemic,caused by SARS-CoV-2,disproportionately affected certain segments of society,particularly the elderly population(which suffered the brunt of the burden of the pandemic in terms of severity of the disease,hospitalization,and death).This study presents a generalized multigroup model,with m heterogeneous sub-populations,to assess the population-level impact of age heterogeneity and vaccination on the transmission dynamics and control of the SARS-CoV-2 pandemic in the United States.Rigorous analysis of the model for the homogeneous case(i.e.,the model with m=1)reveal that its disease-free equilibrium is globally-asymptotically stable for two special cases(with perfect vaccine efficacy or negligible disease-induced mortality)whenever the associated reproduction number is less than one.The model has a unique and globally-asymptotically stable endemic equilibrium,for special a case,when the associated reproduction threshold exceeds one.The homogeneous model was fitted using the observed cumulative mortality data for the United States during three distinct waves(Waves A(October 17,2020 to April 5,2021),B(July 9,2021 to November 7,2021)and C(January 1,2022 to May 7,2022))chosen to align with time periods when the Alpha,Delta and Omicron were,respectively,the predominant variants in the United States.The calibrated model was used to derive a theoretical expression for achieving vaccine-derived herd immunity(needed to eliminate the disease in the United States).It was shown that,using the one-group homogeneous model,vaccine-derived herd immunity is not attainable during Wave C of the pandemic in the United States,regardless of the coverage level of the fully-vaccinated individuals.Global sensitivity analysis was carried out to determine the parameters of the model that have the most influence on the disease dynamics and burden.These analyses reveal that control and mitigation strategies that may be very effective during one wave may not be so very effective during the other wave or waves.However,strategies that target asymptomatic and pre-symptomatic infectious individuals are shown to be consistently effective across all waves.To study the impact of the disproportionate effect of COVID-19 on the elderly population,we considered the heterogeneous model for the case where the total population is subdivided into the sub-populations of individuals under 65 years of age and those that are 65 and older.The resulting two-group heterogeneous model,which was also fitted using the cumulative mortality data for wave C,was also rigorously analysed.Unlike for the case of the one-group model,it was shown,for the two-group model,that vaccine-derived herd immunity can indeed be achieved during Wave C of the pandemic if at least 61%of the populace is fully vaccinated.Thus,this study shows that adding age heterogeneity into a SARS-CoV-2 vaccination model with homogeneous mixing significantly reduces the level of vaccination coverage needed to achieve vaccine-derived herd immunity(specifically,for the heterogeneous model,herd-immunity can be attained during Wave C if a moderate proportion of susceptible individuals are fully vaccinated).The consequence of this result is that vaccination models for SARS-CoV-2 that do not explicitly account for age heterogeneity may be overestimating the level of vaccine-derived herd immunity threshold needed to eliminate the SARS-CoV-2 pandemic.

Dynamics of COVID-19 pandemic in India and Pakistan: A metapopulation modelling approach

India has been the latest global epicenter for COVID-19,a novel coronavirus disease that emerged in China in late 2019.We present a base mathematical model for the transmission dynamics of COVID-19 in India and its neighbor,Pakistan.The base model was rigorously analyzed and parameterized using cumulative COVID-19 mortality data from each of the two countries.The model was used to assess the population-level impact of the control and mitigation strategies implemented in the two countries(notably non-pharmaceutical interventions).Numerical simulations of the basic model indicate that,based on the current baseline levels of the control and mitigation strategies implemented,the pandemic trajectory in India is on a downward trend.This downward trend will be reversed,and India will be recording mild outbreaks,if the control and mitigation strategies are relaxed from their current levels.By early September 2021,our simulations suggest that India could record up to 460,000 cumulative deaths under baseline levels of the implemented control strategies,while Pakistan(where the pandemic is comparatively milder)could see over 24,000 cumulative deaths at current mitigation levels.The basic model was extended to assess the impact of back-and-forth mobility between the two countries.Simulations of the resulting metapopulation model show that the burden of the COVID-19 pandemic in Pakistan increases with increasing values of the average time residents of India spend in Pakistan,with daily mortality in Pakistan peaking in mid-August to mid-September of 2021.Under the respective baseline control scenarios,our simulations show that the backand-forth mobility between India and Pakistan could delay the time-to-elimination of the COVID-19 pandemic in India and Pakistan to November 2022 and July 2022,respectively.