Stability and optimal control analysis of a stage-structured SVIHRS model with isolation, infection based media awareness and media-induced vaccination

Abstract

Sometimes vaccination is reported through media awareness and behavioral responses through different life stages on epidemic outbreaks. But how much awareness is required for effective implementation of vaccination is important from the public health standpoint. To validate this fact, we propose a deterministic SVIHRS stage-structured epidemic model with isolation, infection based media awareness and media-induced vaccination. In the absence of disease, no media campaign is required and hence the disease-free equilibrium exists under a sufficient condition, which is independent of the media awareness coefficient. To study the effect of awareness campaigns by media on the outbreak of an epidemic, a basic reproduction number RV using the next-generation matrix approach is determined, which shows that an endemic equilibrium point exists when RV>1. The local stability of both equilibrium points is analyzed by the corresponding characteristic equations and sufficient conditions are also determined for global stability using Lyapunov second method. A sensitivity analysis for the basic reproduction number is performed to inform target parameters to be controlled. Further, an optimal control problem is studied using Pontryagin’s minimum principle to identify an optimal implementation rate of awareness campaigns so that disease can be controlled with minimal possible expenditure on awareness campaigns. Finally, using MATLAB, some numerical simulations are carried out in support of the stability, sensitivity, and optimal control results.