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.
Threshold dynamics for corotational wave maps
