A theoretical study of mathematical model for the spread of Zika virus disease

Abstract

In this study, we have developed and analyzed as SEIR-SI Zika virus model by considering non-linear incidence for the human to human transmission. The disease transmission rate is taken in the saturated form. This assumption is reasonable as it incorporates the behavioral change of the susceptible individuals and the crowding effect of the infected individuals. Investigate the existence of disease-free and endemic equilibrium points and their stability are discussed in detail. The epidemic threshold parameter $(R_0)$ is computed using the next-generation matrix method and it has seen that the system may possess a phenomenon of backward bifurcation when $R_0$ is less than unity by using Center Manifold Theory. The sensitivity analysis of the leading parameters of the basic reproduction number $R_0$ of the model is investigated. Moreover, the results of the deterministic model are compared using numerical simulations to make the analysis more significant.