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

TL;DR

This paper introduces a generalized SIR model incorporating distributions of inherent susceptibility and external infectivity, revealing their critical role in pandemic dynamics and multiple infection waves, which are not captured by naive models.

Contribution

The study develops a novel SIR model with susceptibility and infectivity distributions, demonstrating their impact on infection estimates and pandemic wave patterns, including multiple peaks.

Findings

Neglecting susceptibility and infectivity distributions overestimates infections.

Inclusion of these distributions alters herd immunity thresholds.

Simulations reproduce multiple infection peaks and complex migration effects.

Abstract

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 ($\sigma_{inh}$) and external infectivity ($\iota_{ext}$), 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 $\sigma_{inh}$ and $\iota_{ext}$ through a new Critical Infection Parameter (CIP) ($\gamma_c$). 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.