Dynamics and optimal control of a Zika model with sexual and vertical transmissions

Hai-Feng Huo; Tian Fu; Hong Xiang; Hai-Feng Huo; Tian Fu; Hong Xiang

doi:10.3934/mbe.2023361

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 5: 8279-8304. doi: 10.3934/mbe.2023361

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Research article

Dynamics and optimal control of a Zika model with sexual and vertical transmissions

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Academic Editor: Tonghua Zhang

Received: 27 November 2022 Revised: 08 February 2023 Accepted: 14 February 2023 Published: 28 February 2023

A new transmission model of Zika virus with three transmission routes including human transmission by mosquito bites, sexual transmission between males and females and vertical transmission is established. The basic reproduction number $ R_{0} $ is derived. When $ R_{0} < 1 $, it is proved that the disease-free equilibrium is globally stable. Furthermore, the optimal control and mitigation methods for transmission of Zika virus are deduced and explored. The MCMC method is used to estimate the parameters and the reasons for the deviation between the actual infection cases and the simulated data are discussed. In addition, different strategies for controlling the spread of Zika virus are simulated and studied. The combination of mosquito control strategies and internal human control strategies is the most effective way in reducing the risk of Zika virus infection.
- Zika virus,
- vertical transmission,
- sexual transmission,
- the basic reproduction number,
- optimal control
Citation: Hai-Feng Huo, Tian Fu, Hong Xiang. Dynamics and optimal control of a Zika model with sexual and vertical transmissions[J]. Mathematical Biosciences and Engineering, 2023, 20(5): 8279-8304. doi: 10.3934/mbe.2023361

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Abstract

A new transmission model of Zika virus with three transmission routes including human transmission by mosquito bites, sexual transmission between males and females and vertical transmission is established. The basic reproduction number $ R_{0} $ is derived. When $ R_{0} < 1 $, it is proved that the disease-free equilibrium is globally stable. Furthermore, the optimal control and mitigation methods for transmission of Zika virus are deduced and explored. The MCMC method is used to estimate the parameters and the reasons for the deviation between the actual infection cases and the simulated data are discussed. In addition, different strategies for controlling the spread of Zika virus are simulated and studied. The combination of mosquito control strategies and internal human control strategies is the most effective way in reducing the risk of Zika virus infection.

References

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