Abstract
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.
Highlights
Zika virus disease or Zika fever is a mosquito-borne disease caused by the Zika virus (ZIKV)
We have developed a compartmental population model to describe the transmission of Zika virus disease in a periodic environment
We have shown that the global dynamics of the model is determined by the basic reproduction number R0
Summary
Zika virus disease or Zika fever is a mosquito-borne disease caused by the Zika virus (ZIKV). This Flavivirus was first identified in monkeys in Uganda in 1947 (Dick et al 1952), identified in humans in 1952 in Uganda and Tanzania (Smithburne 1952). Zika virus is spread in tropical and subtropical regions by the bite of infected female mosquitoes from the Aedes genus (by Aedes aegypti above all) (see, e.g., Petersen et al 2016), the same species that is responsible for dengue, chikungunya and yellow fever transmission. Zika virus is spread via sexual contacts, principally from men to women (Magalhaes et al 2018).
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