Mathematical model for Zika virus dynamics with sexual transmission route

• Published in: Ecological complexity 2017-03, Vol.29, p.61-81
• Main Authors: Agusto, F.B., Bewick, S., Fagan, W.F.
• Format: Article
• Language: English
• Subjects: Backward bifurcation; Heterosexual and homosexual couples; Sexual transmission; Stability; Zika virus
• ISSN: 1476-945X
• DOI: 10.1016/j.ecocom.2016.12.007

•The model disease free equilibrium is locally and globally asymptotically stable.•The model exhibits in the presence of disease induced mortality the phenomenon of backward bifurcation.•The sexual transmission route contributes significantly to the disease burden in the community.•Risky behavior among the male population increases the number of infected individuals in that population. Zika virus is a flavivirus transmitted to humans primarily through the bite of infected Aedes mosquitoes. In addition to vector-borne spread, however, the virus can also be transmitted through sexual contact. In this paper, we formulate and analyze a new system of ordinary differential equations which incorporates both vector and sexual transmission routes. Theoretical analysis of this model when there is no disease induced mortality shows that the disease-free equilibrium is locally and globally asymptotically stable whenever the associated reproduction number is less than unity and unstable otherwise. However, when we extend this same model to include Zika induced mortality, which have been documented in Latin America, we find that the model exhibits a backward bifurcation. Specifically, a stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. To further explore model predictions, we use numerical simulations to assess the importance of sexual transmission to disease dynamics. This analysis shows that risky behavior involving multiple sexual partners, particularly among male populations, substantially increases the number of infected individuals in the population, contributing significantly to the disease burden in the community.