Global dynamics and control strategies of an epidemic model having logistic growth, non-monotone incidence with the impact of limited hospital beds

In this paper, we have considered a deterministic epidemic model with logistic growth rate of the susceptible population, non-monotone incidence rate, nonlinear treatment function with impact of limited hospital beds and performed control strategies. The existence and stability of equilibria as well as persistence and extinction of the infection have been studied here. We have investigated different types of bifurcations, namely Transcritical bifurcation, Backward bifurcation, Saddle-node bifurcation and Hopf bifurcation, at different equilibrium points under some parametric restrictions. Numerical simulation for each of the above-defined bifurcations shows the complex dynamical phenomenon of the infectious disease. Furthermore, optimal control strategies are performed using Pontryagin's maximum principle and strategies of controls are studied for two infectious diseases. Lastly using efficiency analysis we have found the effective control strategies for both cases.

Automated summary

The paper analyzes a deterministic epidemic model with logistic growth rate of susceptible population, non-monotone incidence rate, and nonlinear treatment function with limited hospital bed impact, along with control strategies. It studies the existence, stability, persistence, and extinction of infections, as well as different types of bifurcations at equilibrium points under parametric restrictions. Numerical simulations and optimal control strategies reveal complex dynamics of infectious diseases, leading to effective control strategies for two cases through efficiency analysis.