Modeling the effect of multiple interventions to balance healthcare demand for controlling infectious disease outbreaks

Understanding the impact of information-induced behavioral responses on the public, as well as precise forecasting of hospital bed demand, is critical during infectious disease epidemics to prevent managing healthcare facilities. Hence to study the impact of information-induced behavioral response in the public and the reinfection of diseases on the disease dynamics, we created a nonlinear SIHRZ mathematical model. We calculated the basic reproduction numbers and used mesh and contour plots to investigate the effect of various parameters on disease dynamics. It is observed that even if $\widetilde{R_0}<1$, the disease cannot be eradicated because of reinfection. The most sensitive parameters expected to affect the disease’s endemicity are found by computing the sensitivity indices. The dynamic system has an endemic equilibrium point, which is stable while $\widetilde{R_0}>1$ and unstable when $\widetilde{R_0}<1$. Using the Routh–Hurwitz criterion and the construction of the Lyapunov function, the equilibrium point’s local and global stability is examined. We have further examined the model system for the population’s time lag in immunity loss as a result of the efficacy of medicines, vaccination, self-defense, etc. Due to this delay, an oscillatory nature of the population is obtained. We determined the existence and direction of the Hopf bifurcation, as well as the stability of the equilibrium point, using the delay as a bifurcation parameter. Comprehensive numerical experiments are conducted to explore and validate qualitative results, providing valuable biological insights. This research highlights the critical role that information, treatment intensity, the overall number of hospital beds available, and the occupancy rate of those beds have in determining the behavioral reaction of susceptibles. The model also evaluated cases of fading immunity to look for epidemic peaks. By raising immunization and vaccine effectiveness rates, this peak can be lowered. Moreover, our results suggest that the oscillations that cause problems in managing disease outbreaks would make it extremely difficult to determine the real data of hospitalized and infected individuals. Hence, the WHO, governmental organizations, health policymakers, etc. cannot accurately estimate the scope of an epidemic. As a result, information provided by health authorities and the government regarding disease outbreaks must be kept up to date to limit the disease burden, which is also dependent on funding availability and policymaker decisions.