Global stability analysis of endemic equilibrium point of mathematical model for the transmission and control of Zika Virus disease dynamics

摘要

We constructed Goh Volterra type of Lyapunov function from the transformed model of our formulated mathematical model for the transmission and control of zika virus disease dynamics. Applying the La Salle’s invariance principle to the time derivative of the constructed Lyapunov function confirms the existence of global asymptotic stability of unique endemic equilibrium point of the model. The model is solved using differential transformation method based on two different levels of controls. The Graphical simulations of some vital solutions of the model equations showed the impact of the various control measures incorporated into the model. Moreover, the sensitivity analysis of the sensitive parameters is carried out using the effective reproduction number of the model equations. Various characteristics of the vital state variables and the sensitive parameters provide forecasting premises for any possible outbreak of zika virus disease for effective control measure or containment. This study provides a suitable guide for the containment or control measure of any possible outbreak of zika virus disease. Therefore, with strict adherence to the various measures incorporated into the model equations, the outbreak of zika virus disease can be controlled whenever the effective reproduction number is reduced to less than unity.