Exploring epidemics using non-monotonic incidence function: Effects of sociological factors and hospital bed availability

This study investigates the dynamics of an epidemic employing an (Susceptible-Infected-Hospitalized-Recovered-Susceptible (SIHRS) epidemiological model highlighting the crucial importance of hospital bed availability and a non-monotone incidence function, which incorporates the influences of stringent governmental measures, social behavior dynamics and public responses in both autonomous and non-autonomous scenarios. The analysis investigates the conditions for existence of infection-free and endemic steady states based on the basic reproduction number as it surpasses unity. Sensitivity analysis has been conducted to evaluate the impact of different system parameters on disease transmission. This work also investigates alterations in stability of the system caused by transcritical, Hopf and saddle-node bifurcations. Additionally, two-parameter bifurcation identifies the regions where the stability of both the equilibrium points has been examined. Numerical simulations are shown to illustrate all the theoretically obtained results. Also, the model examines the dynamical behavior of the epidemic when the quantity of available hospital beds varies periodically. This aspect of the study highlights the significant impact of hospital bed availability. Such factors are crucial in preventing disease spread during an epidemic. The results provide valuable insights into how dynamic patterns of disease transmission are influenced by healthcare infrastructure and public health interventions. This comprehensive exploration underscores the importance of integrated approaches combining medical resources and societal measures in managing and mitigating the effects of epidemics.