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 neighbour, Pakistan. The base model, which takes the form of a deterministic system of nonlinear differential equations, is 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 community lockdowns, use of face masks, and social-distancing). 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 (as characterized by the reproduction number of the disease dynamics in India below, but close to, unity). This downward trend will be reversed, and India will be recording mild outbreaks (i.e., pandemic waves), if the control and mitigation strategies are relaxed from their current levels (e.g., relaxed to the extent that the associated community transmission parameters are increased by 20% or 40% from their current baseline values). Our simulations suggest that India could record up to 460,000 cumulative deaths by early September 2021 under the baseline levels of the control strategies implemented (up to 25,000 of the projected deaths could be averted if the control and mitigation measures are strengthened to the extent that the associated community transmission parameters are reduced by 20% from their baseline values). Our simulations show that the pandemic in Pakistan is much milder, with an estimated projected cumulative mortality of about 24,000 by early September 2021 under the baseline scenario. 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. In particular, it is shown that the India- to-Pakistan mobility pattern may trigger a fourth wave of the pandemic in Pakistan (under certain mobility scenarios), with daily mortality 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 the two countries by three to five months (specifically, under the respective baseline scenarios, elimination could be delayed in India and Pakistan to November 2022 and July 2022, respectively).