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.

Mathematics of a single-locus model for assessing the impacts of pyrethroid resistance and temperature on population abundance of malaria mosquitoes

This study presents a genetic-ecology modeling framework for assessing the combined impacts of insecticide resistance,temperature variability,and insecticide-based interventions on the population abundance and control of malaria mosquitoes by genotype.Rigorous analyses of the model we developed reveal that the boundary equilibrium with only mosquitoes of homozygous sensitive(resistant)genotype is locally-asymptotically stable whenever a certain ecological threshold,denoted by R^(SS)_(0) eR^(RR)_(0) T,is less than one.Furthermore,genotype i drives genotype j to extinction whenever R j 0>1 and R i 0<1(where i,j SS or RR,with i s j).The model exhibits the phenomenon of bistability when both thresholds are less than one.In such a bistable situation,convergence to any of the two boundary equilibria depends on the initial allele distribution in the state variables of the model.Furthermore,in this bistable case,where maxfR^(SS)_(0);R^(RR)_(0)g<1,the basin of attraction of the boundary equilibrium of the mosquito genotype with lower value of the ecological threshold is larger.Specifically,the basin of attraction of the boundary equilibrium for genotype i is larger than that of genotype j if R^(i)_(0)<R^(j)_(0)<1.When both ecological thresholds exceed one eminfR^(SS)_(0);R^(RR)_(0)g>1T,the two boundary equilibria lose their stability,and a coexistence equilibrium(where all three mosquito genotypes coexist)becomes locally-asymptotically stable.Global sensitivity analysis shows that the key parameters that greatly influence the dynamics and population abundance of resistant mosquitoes include the proportion of new adult mosquitoes that are females,the insecticide-induced mortality rate of adult female mosquitoes,the coverage level and efficacy of adulticides used in the community,the oviposition rates for eggs of heterozygous and homozygous resistant genotypes,and the modification parameter accounting for the reduction in insecticide-induced mortality due to resistance.Numerical simulations show that the adult mosquito population increases with increasing temperature until a peak is reached at 31C,and declines thereafter.Simulating the model for moderate and high adulticide coverage,together with varying fitness costs of resistance,shows a switch in the dominant genotype at equilibrium as temperature is varied.In other words,this study shows that,for certain combinations of adulticide coverage and fitness costs of insecticide resistance,increases in temperature could result in effective management of resistance(by causing the switch from a stable resistant-only boundary equilibrium(at 18C)to a stable sensitive-only boundary equilibrium(at 25C)).Finally,this study shows that,for moderate fitness costs of resistance,density-dependent larval mortality suppresses the total population of adult mosquitoes with the resistant allele for all temperature values in the range[18Ce36C].