Bifurcation and basin stability of an SIR epidemic model with limited medical resources and switching noise

Considering the sudden change of environmental disturbance, a stochastic susceptible infectious recov-ered (SIR) model with Markov jump and the limited medical resources is proposed. Firstly, by a bifurca-tion analysis of the deterministic SIR model, the maximal medical resource tipping point can be detected to adjust and optimize the medical resource allocation. Then, the impact of environmental disturbance on the basin stability is explored via the first escape probability(FEP). Based on the stochastic averaging of Markov jump process, the SIR epidemic system with switching random excitation is transferred into a probability-weighted Ito stochastic differential equation. Furthermore, the theoretical FEP is solved by the finite difference method and the validity is verified by numerical simulation. It is worth noting that the increase of noise intensity can decrease the basin stability of SIR model, and the existence of switching noise makes a difference in the basin stability compared with the epidemic system without switching intensity. (c) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This study proposes a stochastic SIR model with Markov jump and limited medical resources to address environmental disturbances. By analyzing the system through bifurcation and first escape probability, it was found that the increase in noise intensity can decrease system stability, with switching noise having an impact on stability compared to systems without it.