Dynamical aspects of a delayed epidemic model with subdivision of susceptible population and control strategies

Abstract

A delay epidemic model is developed, with the susceptible population divided into three subclasses. In the main model, the well-known “Michaelis Menten Equation” is utilized to represent the effect of saturation. Infected, unaware, partially aware, and fully conscious compartments are included in the saturation incidence rates. The model includes a time delay to demonstrate the occurrence of Hopf Bifurcation. Following the formulation of a delay epidemic model, the local stability and the presence of Hopf bifurcation are investigated. The direction and stability of the Hopf bifurcation are then investigated. Furthermore, the Nyquist criterion is used to estimate the length of the time delay in order to maintain stability. An example is also presented to highlight the current research work's findings. Finally, appropriate control techniques are introduced to aid policymakers in disease control. The “Pontryagin's maximum principle” is the major tool utilized in the optimal control part.