Stability Analysis of Disease-Free Equilibrium Point for Transmission and Control of Zika Virus Fever Dynamics

Abstract

We give the overview of the dynamics of the transmission and control of zika virus fever in the paper. Four mediums of transmission and control are incorporated into the formulated mathematical model of the virus dynamics. The effective reproduction number is obtained from the model equations. The local stability of disease free equilibrium point of the model is analyzed using reduced, linearized Jacobian matrix if the effective reproduction number is less than one and the global stability is also analyzed using the constructed Lyapunov function if the effective reproduction number is less or equal to one. The epidemiological implication of the analysis shows that zika virus fever can be controlled.