Mathematical analysis of Yellow Fever transmission dynamics using Wolbachia and vaccination as control strategies

Abstract

We present the mathematical analysis of yellow fever transmission dynamics using
Wolbachia and vaccination as the control strategies. A deterministic ordinary differential
equation model for yellow fever disease transmission dynamics within the human and
mosquito populations is formulated. The model equilibrium points were obtained, while
the criteria for their macrocosm and stability were investigated. Numerical simulations were carried out using a classical fourth order Runge-kutta method in MATLAB. From the simulations, we investigated and established that the disease can only be eradicated in our society if we encourage the populace to take the vaccines against the disease in the case of the disease insurgence. This is primarily due to the fact that the vaccinated humans do not respond to the infectivity of the Wolbachia-free mosquitoes’ biting. Also effective, efficient and timely treatment of infectious persons must be carried out if we must contain
the disease when it occurs.