Influence of seasonality on Zika virus transmission

In order to study the impact of seasonality on Zika virus dynamics, we analyzed a non-autonomous mathematical model for the Zika virus (ZIKV) transmission where we considered time-dependent parameters. We proved that the system admitted a unique bounded positive solution and a global attractor set. The basic reproduction number, ${\mathcal{R}}_0$, was defined using the next generation matrix method for the case of fixed environment and as the spectral radius of a linear integral operator for the case of seasonal environment. We proved that if ${\mathcal{R}}_0$ was smaller than the unity, then a disease-free periodic solution was globally asymptotically stable, while if ${\mathcal{R}}_0$ was greater than the unity, then the disease persisted. We validated the theoretical findings using several numerical examples.