Delay Infectivity and Delay Recovery SIR model

TL;DR

This paper introduces a delay-infected and delay-recovery SIR model derived from continuous time random walk theory, capturing incubation effects and complex dynamics without adding new compartments.

Contribution

It presents a novel derivation of delay differential equations for the SIR model using a continuous time random walk framework, ensuring physical consistency.

Findings

The model captures diverse dynamical behaviors.

It accounts for incubation effects without extra compartments.

Provides new insights into disease spread dynamics.

Abstract

We have derived the governing equations for an SIR model with delay terms in both the infectivity and recovery of the disease. The equations are derived by modelling the dynamics as a continuous time random walk, where individuals move between the classic SIR compartments. With an appropriate choice of distributions for the infectivity and recovery processes delay terms are introduced into the governing equations in a manner that ensures the physicality of the model. This provides novel insight into the underlying dynamics of an SIR model with time delays. The SIR model with delay infectivity and recovery allows for a more diverse range of dynamical behaviours. The model accounts for an incubation effect without the need to introduce new compartments.