Dynamical System of Zikav Disease Spread Through The Isolation with Two Groups of Infected Population

Abstract

A viral disease ZIKAV (Zika virus) caused by a type of a Flavivirus closely related to dengue is primarily transmitted to humans by the bites of infected mosquitoes from the Aedes aegypti. Seeking to understand the dynamics of spread of the ZIKAV disease, we propose SEIIJRV1V2V3 mathematical models for vector transmission of the virus, sexual contact transmission, isolation, and conducted stability analysis. Isolation is one of the ways to disease control. This isolation is done on symptomatic-infected human population to prevent the spread of the disease. We calculate the basic reproduction number R0 and show that for R0 < 1, the disease-free equilibrium is locally asymtotically stable. In addition, it is shown that for a special case when R0 > 1, the endemic equilibrium is locally asymptotically stable. Numerical simulations are shown to support the analytical results and allow us to have a clear view of the effect of isolation.