On SIR epidemic models with feedback-controlled interactions and network effects

TL;DR

This paper extends the classical SIR epidemic model by incorporating feedback-controlled contact rates and network effects, analyzing threshold phenomena and control strategies in epidemic spread.

Contribution

It introduces a generalized SIR model with arbitrary feedback functions for contact rates and explores network interactions among subpopulations.

Findings

Existence of a threshold phenomenon in generalized models

Analysis of discontinuous feedback using sliding mode control

Preliminary simulations of network SIR models

Abstract

We study extensions of the classical SIR model of epidemic spread. First, we consider a single population modified SIR epidemics model in which the contact rate is allowed to be an arbitrary function of the fraction of susceptible and infected individuals. This allows one to model either the reaction of individuals to the information about the spread of the disease or the result of government restriction measures, imposed to limit social interactions and contain contagion. We study the effect of both smooth dependancies of the contact rate for which we prove the existence of a threshold phenomenon that generalizes the well-known dichotomy associated to the reproduction rate parameter in the classical SIR model, and discontinuous feedback terms, which can be studied using tools from sliding mode control. Finally, we consider network SIR models involving different subpopulations that interact on a contact graph and present some preliminary simulations of modified versions of the classic SIR network.