Effects of Nonmonotonic Functional Responses on a Disease Transmission Model: Modeling and Simulation.

Abstract

In this article, a novel susceptible-infected-recovered epidemic model with nonmonotonic incidence and treatment rates is proposed and analyzed mathematically. The Monod-Haldane functional response is considered for nonmonotonic behavior of both incidence rate and treatment rate. The model analysis shows that the model has two equilibria which are named as disease-free equilibrium (DFE) and endemic equilibrium (EE). The stability analysis has been performed for the local and global behavior of the DFE and EE. With the help of the basic reproduction number $\left(R_0\right)$ , we investigate that DFE is locally asymptotically stable when $R_0<1$ and unstable when $R_0>1$ . The local stability of DFE at $R_0=1$ has been analyzed, and it is obtained that DFE exhibits a forward transcritical bifurcation. Further, we identify conditions for the existence of EE and show the local stability of EE under certain conditions. Moreover, the global stability behavior of DFE and EE has been investigated. Lastly, numerical simulations have been done in the support of our theoretical findings.