Transmission Dynamics of Zika Fever: A SEIR Based Model

In this paper, a deterministic model is proposed to perform a thorough investigation of the transmission dynamics of Zika fever. Our model, in particular, takes into account the effects of horizontal as well as vertical disease transmission of both humans and vectors. The expression for basic reproductive number R is determined in terms of horizontal and vertical disease transmission rates. An in-depth stability analysis of the model is performed, and it is shown, that model is locally asymptotically stable when R< 1. In this case, there is a possibility of backward bifurcation in the model. With the assumption that total population is constant, we prove that the disease free state is globally asymptotically stable when R< 1. It is also shown that disease strongly uniformly persists when R> 1 and there exists an endemic equilibrium which is unique if the total population is constant. The endemic state is locally asymptotically stable when R> 1.