Bifurcations and the exchange of stability with coinfection

TL;DR

This paper analyzes how bifurcations affect the stability and dynamics of a two-pathogen SIR model with coinfection, partial cross-immunity, and density-dependent growth, revealing complex transition scenarios.

Contribution

It introduces a generalized SIR model allowing coinfected individuals to transmit only one disease and performs a bifurcation analysis to explore stability changes.

Findings

Existence of a stable equilibrium branch parameterized by carrying capacity K

Bifurcation points lead to changes in disease compartment presence

Different parameter regimes produce diverse transition scenarios

Abstract

We perform a bifurcation analysis on an SIR model involving two pathogens that influences each other. Partial cross-immunity is assumed and coinfection is thought to be less transmittable then each of the diseases alone. The susceptible class has density dependent growth with carrying capacity $K$. Our model generalizes the model developed in our previous papers by introducing the possibility for coinfected individuals to spread only one of the diseases when in contact with a susceptible. We perform a bifurcation analysis and prove the existence of a branch of stable equilibrium points parmeterized by $K$. The branch bifurcates for some $K$ resulting in changes in which compartments are present as well as the overall dynamics of the system. Depending on the parameters different transition scenarios occur.