Dynamics of SIR model with heterogeneous response to intervention policy

TL;DR

This paper analyzes a modified SIR epidemic model incorporating individual heterogeneity in response to interventions, using Preisach hysteresis operators, revealing how heterogeneity affects epidemic equilibrium and peak infection levels.

Contribution

It introduces a novel SIR model with heterogeneous responses modeled by Preisach hysteresis, extending understanding of epidemic dynamics under variable individual behaviors.

Findings

Heterogeneity influences the epidemic's limit points and infection peaks.

The model compares heterogeneous responses to a uniform response scenario.

Different levels of heterogeneity lead to distinct epidemic trajectories.

Abstract

We study dynamics of a variant of the SIR the model, where we assume that individuals respond differently to dynamics of the epidemic. Their heterogeneous response is modeled by the Preisach hysteresis operator. The degree of heterogeneity of the response is measured by the variance $\sigma^2$ of the corresponding distribution (the Preisach density function). The proposed model has a continuum of endemic equilibrium states characterized by different proportions of susceptible, infected and recovered populations. We consider how the limit point of the epidemic trajectory and the infection peak along this trajectory depend on $\sigma$. The heterogeneous model is compared to the the switched model with an ideally uniform response corresponding to $\sigma=0$.