Threshold Dynamics in a Model for Zika Virus Disease with Seasonality

Abstract

AbstractWe present a compartmental population model for the spread of Zika virus disease including sexual and vectorial transmission as well as asymptomatic carriers. We apply a non-autonomous model with time-dependent mosquito birth, death and biting rates to integrate the impact of the periodicity of weather on the spread of Zika. We define the basic reproduction number $${\mathscr {R}}_{0}$$ R 0 as the spectral radius of a linear integral operator and show that the global dynamics is determined by this threshold parameter: If $${\mathscr {R}}_0 < 1,$$ R 0 < 1 , then the disease-free periodic solution is globally asymptotically stable, while if $${\mathscr {R}}_0 > 1,$$ R 0 > 1 , then the disease persists. We show numerical examples to study what kind of parameter changes might lead to a periodic recurrence of Zika.