We 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 \({\mathscr {R}}_{0}\) as the spectral radius of a linear integral operator and show that the global dynamics is determined by this threshold parameter: If \({\mathscr {R}}_0 < 1,\) then the disease-free periodic solution is globally asymptotically stable, while if \({\mathscr {R}}_0 > 1,\) then the disease persists. We show numerical examples to study what kind of parameter changes might lead to a periodic recurrence of Zika.

我们提出了寨卡病毒病传播的区室人口模型，包括性传播和媒介传播以及无症状携带者。我们应用具有时间依赖的蚊子出生、死亡和叮咬率的非自主模型来整合天气周期性对寨卡病毒传播的影响。我们将基本再生数\({\mathscr {R}}_{0}\) 定义为线性积分算子的谱半径，并表明全局动力学由该阈值参数决定：如果\({\mathscr { R}}_0 < 1,\)那么无病周期解是全局渐近稳定的，而如果\({\mathscr {R}}_0 > 1,\)然后疾病持续存在。我们展示了数值例子来研究什么样的参数变化可能导致寨卡病毒的周期性复发。