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Two factors that are often ignored but could play a crucial role in theprogression of an infectious disease are the distributions of inherentsusceptibility ($\sigma_{inh}$) and external infectivity ($\iota_{ext}$), in agiven population. While the former is determined by the immunity of anindividual towards a disease, the latter depends on the duration of exposure tothe infection. We model the spatio-temporal propagation of a pandemic using ageneralized SIR (Susceptible-Infected-Removed) model by introducing thesusceptibility and infectivity distributions to understand their combinedeffects, which appear to remain inadequately addressed till date. We considerthe coupling between $\sigma_{inh}$ and $\iota_{ext}$ through a new CriticalInfection Parameter (CIP) ($\gamma_c$). We find that the neglect of thesedistributions, as in the naive SIR model, results in an overestimation of theamount 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 bylong-range migration. We solve the resulting master equations by performingKinetic Monte Carlo Cellular Automata (KMC-CA) simulations. Importantly, oursimulations can reproduce the multiple infection peak scenario of a pandemic.The latent interactions between disease migration and the distributions ofsusceptibility and infectivity can render the progression a character vastlydifferent from the naive SIR model. In particular, inclusion of theseadditional features renders the problem a character of a living percolatingsystem where the disease cluster survives by migrating from region to region.

Origin of Multiple Infection Waves in a Pandemic: Effects of Inherent Susceptibility and External Infectivity Distributions