SIS and SIR epidemic models under virtual dispersal

TL;DR

This paper introduces a novel multi-group epidemic modeling framework based on virtual dispersal, which simplifies contact rate measurement and reveals how dispersal behavior influences disease dynamics across patches.

Contribution

The paper develops a new epidemic modeling approach using residence times, providing insights into disease spread without traditional contact rate assumptions and analyzing its effects on multi-patch epidemic dynamics.

Findings

Global stability of endemic or disease-free states depending on R0

Dispersal behavior significantly affects local disease dynamics

Framework applicable to various endemic and outbreak models

Abstract

In this paper, we develop a multi-group epidemic framework via virtual dispersal where the risk of infection is a function of the residence time and local environmental risk. This novel approach eliminates the need to define and measure contact rates that are used in the traditional multi-group epidemic models with heterogeneous mixing. We apply this approach to a general $n$-patch SIS model whose basic reproduction number $\mathcal R_0 $ is computed as a function of a patch residence-times matrix $\mathbb P$. Our analysis implies that the resulting $n$-patch SIS model has robust dynamics when patches are strongly connected: there is a globally stable endemic equilibrium when $\mathcal R_0>1 $ while the disease free equilibrium is globally stable when $\mathcal R_0\leq1 $. Our further analysis indicates that the dispersal behavior described by the residence-times matrix $\mathbb P$ has profound effects on the disease dynamics at the single patch level with consequences that proper dispersal behavior along with the local environmental risk can either promote or eliminate the endemic in particular patches. Our work highlights the impact of residence times matrix if the patches are not strongly connected. Our framework can be generalized in other endemic and disease outbreak models. As an illustration, we apply our framework to a two-patch SIR single outbreak epidemic model where the process of disease invasion is connected to the final epidemic size relationship. We also explore the impact of disease prevalence driven decision using a phenomenological modeling approach in order to contrast the role of constant versus state dependent $\mathbb P$ on disease dynamics.