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**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 |

### Keywords:

disease-free equilibrium; stability analysis; sensitivity analysis; basic reproduction number; sexual transmission
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\textit{T. Barve} et al., South East Asian J. Math. Math. Sci. 18, No. 2, 87--98 (2022; Zbl 1513.34174)

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### References:

[1] | Agusto F. B., Bewick S. & Fagan W. F., Mathematical model of Zika virus with vertical transmission, Infectious Disease Modelling, 2 (2) (2017), 244-267. |

[2] | Bañuelos S., Martinez M. V., Mitchell C., & Prieto Langarica A., Using mathematical modelling to investigate the effect of the sexual behaviour of asymptomatic individuals and vector control measures on Zika, Letters in Biomathematics, 6 (1) (2019), 1-19. |

[3] | Castillo-Chavez C., Feng Z. and Huang W., On the Computation of R 0 and Its Role on Global Stability, In: Mathematical Approaches for Emerging and Reemerging Infectious Diseases: An Introduction, Springer-Verlag, New York, 2002, 229-250. · Zbl 1021.92032 |

[4] | Chitins, N., Hyman, J.M. & Cushing, J. M., Determining Important Pa-rameters in the Spread of Malaria Through the Sensitivity Analysis of a Mathematical Model, Bull. Math. Biol., 70, 1272 (2008). · Zbl 1142.92025 |

[5] | Counotte, M. J., Kim, C. R., Wang, J., Bernstein, K., Deal, C. D., Broutet, N., & Low, N., Sexual transmission of Zika virus and other flaviviruses: A living systematic review, PLoS medicine, 15 (7) (2018), e1002611. |

[6] | Ding, C., Tao, N., & Zhu, Y., A mathematical model of Zika virus and its optimal control, 2016 35th Chinese Control Conference (CCC), (2016), 2642-2645. |

[7] | Herbert W. H., The Mathematics of Infectious Diseases, Society for Industrial and Applied Mathematics, 42( 4) (2000), 599-653. · Zbl 0993.92033 |

[8] | Heffernan J. M., Smith R. J. and Wahl L. M., Perspectives on the basic reproductive ratio, J. R. Soc. Interface, 2 (2005), 281-293. |

[9] | Kibona, I. E. and Yang, C. H., SIR Model of Spread of Zika Virus Infections: ZIKV Linked to Microcephaly Simulations, Health, 9 (2017), 1190-1210. |

[10] | Martins, M. M., Medronho, R. A., & Cunha, A., Zika virus in Brazil and worldwide: a narrative review, Paediatrics and international child health, (2020), 1-8. |

[11] | May M., Relich R. F., A Comprehensive Systems Biology Approach to Study-ing Zika Virus, PLoS ONE, 11 (9), (2016), e0161355. |

[12] | Momoh A., Fügenschuh A., Optimal control of intervention strategies and cost effectiveness analysis for a Zika virus model, Operations Research for Health Care, Vol. 18 (2018), 99-111. |

[13] | Mpeshe, S. C., Nyerere, N., Sanga, S., Modeling approach to investigate the dynamics of Zika virus fever: A neglected disease in Africa, Int. J. Adv. Appl. Math. and Mech., 4 (3) (2017), 14 -21. · Zbl 1382.92244 |

[14] | Pizza, D., Loaiza, A., Arias, O., Sossa, V., Muñoz, C., Osorio, S., Contreras, H., Montoya, J., Patiño, G., Contreras, I., Perea, M., Guerra, M. and García, J., A Simulation Model for the Risk of Fetal Exposure Originated by the Zika Virus (VIZK), Health, 8 (2016), 1178-1186. |

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