Mathematical model for Zika virus dynamics with sexual transmission route |
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Affiliation: | 1. Department of Mathematics, Faculty of Science,Taif University, Taif, 26571, Saudi Arabia;2. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, 44519, Egypt;3. Department of Mathematics, Faculty of Science, Al-Azher University, Nasr City, 11884, Egypt;4. Department of Mathematics, Faculty of Science, Bisha University, Bisha, 61922, Saudi Arabia;5. Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf, Egypt;1. Department of Ecology and Evolutionary Biology, University of Kansas, USA;2. Department of Mathematics, City University of Science and Information Technology, 25000, KP, Pakistan |
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Abstract: | 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. |
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Keywords: | Zika virus Heterosexual and homosexual couples Sexual transmission Stability Backward bifurcation |
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