A nonlinear dynamical model for Zika virus transmission with media awareness and optimal control

Abstract

In order to investigate the dynamics of Zika virus transmission in a human-mosquito population, a nonlinear dynamical system that takes into account the impact of media awareness on disease transmission is suggested. The mosquito population is made up of susceptible and infectious classes with logistic growth, whereas the human population is separated into susceptible, exposed, infected, and recovered compartments. The model's basic qualitative characteristics, such as positivity and boundedness of solutions, are proven. The local stability of the disease-free equilibrium is examined, and the fundamental reproduction number $\mathcal{R}_0$ is determined. Sufficient conditions for backward bifurcation at $\mathcal{R}_0 = 1$ are found, and the presence and uniqueness of the endemic equilibrium are examined. The important factors affecting the spread of disease are found through sensitivity analysis utilizing partial rank correlation coefficients. Additionally, Pontryagin's Maximum Principle is used to derive the requisite optimality requirements for an optimal control issue that incorporates vector control and treatment procedures. To bolster the analytical findings and show how well integrated intervention techniques work to lower the prevalence of infection, numerical simulations are run.