Global Stability of Zika Virus Dynamics

The few mathematical models available in the literature to describe the dynamics of Zika virus are still in their initial stage of stability and bifurcation analysis, and they were in part developed as a response to the most recent outbreaks, including the one in Brazil in 2015, which has also given more hints to its association with Guillain-Barre Syndrome (GBS) and microcephaly. The interaction between and the effects of vector and human transmission are a central part of these models. This work aims at extending and generalizing current research on mathematical models of Zika virus dynamics by providing rigorous global stability analyses of the models. In particular, for disease-free equilibria, appropriate Lyapunov functions are constructed using a compartmental approach and a matrix-theoretic method, whereas for endemic equilibria, a relatively recent graph-theoretic method is used. Numerical evidence of the existence of a transcritical bifurcation is also discussed.