2020/12/30 by Saumyak Mukherjee, Mukherjee, Saumyak, Sayantan Mondal +3
Mathematics · #COVID-19 epidemiological studies #FOS: Biological sciences #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.2012.15053
openalex publication_date 2020/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two factors that are often ignored but could play a crucial role in the progression of an infectious disease are the distributions of inherent susceptibility (σinh) and external infectivity (ιext), in a given population. While the former is determined by the immunity of an individual towards a disease, the latter depends on the duration of exposure to the infection. We model the spatio-temporal propagation of a pandemic using a generalized SIR (Susceptible-Infected-Removed) model by introducing the susceptibility and infectivity distributions to understand their combined effects, which appear to remain inadequately addressed till date. We consider the coupling between σinh and ιext through a new Critical Infection Parameter (CIP) (γc). We find that the neglect of these distributions, as in the naive SIR model, results in an overestimation of the amount of infection in a population, which leads to incorrect (higher) estimates of the infections required to achieve the herd immunity threshold. Additionally, we include the effects of seeding of infection in a population by long-range migration. We solve the resulting master equations by performing Kinetic Monte Carlo Cellular Automata (KMC-CA) simulations. Importantly, our simulations can reproduce the multiple infection peak scenario of a pandemic. The latent interactions between disease migration and the distributions of susceptibility and infectivity can render the progression a character vastly different from the naive SIR model. In particular, inclusion of these additional features renders the problem a character of a living percolating system where the disease cluster survives by migrating from region to region.