Nonlinear dynamics of an SIRS model with ratio-dependent incidence and saturated treatment function.

This article proposes and analyzes an SIRS infectious disease model with ratio-dependent incidence rate and saturated treatment rate functions. The incorporation of a ratio-dependent incidence rate provides a more intricate depiction of disease dynamics, encompassing not just the inhibitory effect of infected individuals but also the presence of susceptible individual for potential infection. Through the analysis of the model, it is discovered that when treatment capacity is limited, the infected population may survive even if the basic reproduction number is less than one. Consequently, the model displays endemicity through the coexistence of multiple steady states, and we observe a backward bifurcation. Further, a geometric approach is applied to derive the global stability of the endemic steady state. Bi-stability, Hopf bifurcation, and saddle-node bifurcation are some examples of nonlinear dynamics that are investigated. Additionally, this study also highlights the existence of Hopf bifurcation for the basic reproduction number less than one, showcasing the rare dynamics associated with ratio-dependent incidence rate function. We give numerical examples to demonstrate and validate the outcomes of our theoretical analysis. [ABSTRACT FROM AUTHOR]