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 back-and-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.