Bifurcation Analysis of a Modified SIR-Based COVID-19 Model with Nonlinear Incidence and Recovery Rates

Abstract

In this work, a Susceptible-Infected-Recovered (SIR)-based epidemic model incorporating nonlinear incidence and recovery rates, with the consideration of limited medical resources (e.g., the availability of hospital beds) is examined. The model also emphasises the significance of factoring in distinct intervention strategies and considers some important epidemiological factors, in the light of COVID-19 endemicity. In particular, the study employs a Monod-type nonlinear incidence rate coupled with a nonlinear recovery equation, to uncover the intricate dynamics that emerge from the interplay of these epidemiological forces. The findings reveal the existence of disease-free and endemic equilibria, their stability conditions, and bifurcational changes in the dynamics of the system. Bifurcation analysis demonstrates the emergence of transcritical, saddle-node and Hopf bifurcations with the existence of distinct stable and unstable equilibria and limit cycles. Overall, this work highlights the importance of mathematical modeling and dynamical systems techniques in investigating the interplay among various epidemiological factors, thereby providing valuable insights to guide effective epidemic control strategies.