## A mathematical model for the sexual transmission of zika virus based on gender and symptoms.(English)Zbl 1513.34174

Summary: Zika virus is a member of Flaviviridae that also causes Japanese Encephalitis, dengue, yellow fever, and West Nile fever. General symptoms of the zika virus are low-grade fever (less than 38.5°), macula-papular rash, myalgia, asthenia, headache, and transient arthritis. Zika virus can cause congenital anomalies (such as microcephaly), Guillain-Barre syndrome, and other neurological and autoimmune disorders. In the present mathematical model, we observed the effect of sexual transmission on gender and symptoms based division of the infected human population. We proposed a theorem to check the local stability of disease free equilibrium state. To verify the theorem, we performed some numerical simulations. We also analyzed the global stability of disease free equilibrium state. Furthermore, we checked the effect of different sexual transmission rates on the population dynamics by calculating normalized sensitivity indices of $$R_0$$. Results of the present study suggest that sexual transmission noticeably affects Zika dissemination and by controlling sexual transmission rates, we can restrict the Zika virus spread.

### MSC:

 34C60 Qualitative investigation and simulation of ordinary differential equation models 34D20 Stability of solutions to ordinary differential equations 34D23 Global stability of solutions to ordinary differential equations 92D30 Epidemiology 34D05 Asymptotic properties of solutions to ordinary differential equations
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### References:

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