Epidemic dynamics in inhomogeneous populations and the role of superspreaders

Abstract

A variant of the SIR model for an inhomogeneous population is introduced in order to account for the effect of variability in susceptibility and infectiousness across a population. An initial formulation of this dynamics leads to infinitely many differential equations. Our model, however, can be reduced to a single first-order one-dimensional differential equation. Using this approach, we provide quantitative solutions for different distributions. In particular, we use GPS data from ~107 cellphones to determine an empirical distribution of the number of individual contacts and use this to infer a possible distribution of susceptibility and infectivity. We quantify the effect of superspreaders on the early growth rate R0 of the infection and on the final epidemic size, the total number of people who are ever infected. We discuss the features of the distribution that contribute most to the dynamics of the infection.

Herd immunity under individual variation and reinfection

“…After completion of this work, similar ideas for capturing individual variation with mean-field epidemic models were elaborated (Britton et al 2020;Di Lauro et al 2021;Kawagoe et al 2021;Neipel et al 2020;Rose et al 2021;Tkachenko et al 2021). These recent developments were largely prompted by the COVID-19 pandemic.…”

“…In addition the authors show that other initial distributions converge towards gamma through the process of contagion. Other authors (Kawagoe et al 2021) derive epidemic final sizes assuming alternative distributions of susceptibility, considering in addition that infectivity may exhibit some correlation with susceptibility (such as in the variable connectivity models analyzed here). They compare numerical results for gamma and lognormal distributions with those obtained using an empirical distribution of individual contacts derived from cell phone geolocation data.…”

“…Individuals who are more susceptible or more exposed to infection are prone to be infected and become immune earlier. As a result, earlier episodes contribute disproportionately to herd immunity as they remove highly susceptible and exposed subjects from the susceptible pool (Ferrari et al 2006;Britton et al 2020;Kawagoe et al 2021;Neipel et al 2020;Rose et al 2021;Gomes et al 2022;Aguas et al 2021).…”

A high-resolution flux-matrix model describes the spread of diseases in a spatial network and the effect of mitigation strategies

“…Epidemic outbreaks in the last two decades have provided the scientific community with a wealth of material to study these questions, going beyond the classic Susceptible-Infected-Recovered (SIR) theory with perfect mixing [2][3][4][5][6]. Several studies have shown how the total epidemic size can be affected by factors such as inhomogeneity in transmission rates [7][8][9][10][11][12][13][14] or in the mode of transmission [15,16]. Classically, motion of individuals was taken into account by introducing diffusion terms in the standard SIR equations, allowing the emergence of spatio-temporal patterns [17][18][19][20].…”