Dynamical Analysis for A Simple Model of Zika Virus Transmission

Puji Andayani
Universitas Internasional Semen Indonesia, Kompleks PT.Semen Indonesia (Persero) Tbk, Jalan Veteran, Gresik, Indonesia
Email: puji.andayani@uisi.ac.id

The purpose of this work is to study the stability of a vector-borne model of Zika virus. According to the parameters of the model, there are two equilibrium, namely disease-free equilibrium (DFE) and endemic equilibrium (END). We first provide some sufficient conditions that guarantee the existence of positive equilibriums for the system. The existence of endemic equilibrium and disease-free equilibrium are determined according to the basic reproduction number. Then we show that all solutions of the system are bounded when the initial values are in the first quadrant. Next, we analyze the local stability of the equilibrium by using the standard method of ODE. We also perform some numerical simulations to support the analytical results. The numerical results show that the solutions of the model exhibit the global stable.

Keywords: Zika virus, vector-borne, stability, basic reproduction number

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