Dynamic analysis and optimal control of Zika virus transmission with immigration

Zongmin Yue; Yitong Li; Fauzi Mohamed Yusof; Zongmin Yue; Yitong Li; Fauzi Mohamed Yusof

doi:10.3934/math.20231116

AIMS Mathematics

2023, Volume 8, Issue 9: 21893-21913. doi: 10.3934/math.20231116

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Dynamic analysis and optimal control of Zika virus transmission with immigration

1.
Department of Mathematics, Shaanxi University of Science and Technology, Xi'an, 710021, China
2.
Faculty of Science and Mathematics, Sultan Idris Education University, Tanjong Malim, Malaysia

Received: 27 March 2023 Revised: 07 June 2023 Accepted: 28 June 2023 Published: 10 July 2023
MSC : 34D23, 34D20, 34D45, 92B05

In this paper, a type of Zika virus model with immigration is considered. Additionally based on the risk of infected immigrants, we propose a control measure of screening for immigrants and a three-measure control model of combined mosquito prevention and killing. The existence and stability of the equilibrium in the Zika virus model are analyzed. The necessary conditions for the existence of the optimal solution are given using Pontryagin's maximum principle. We focused on testing screening of the immigrating population to ensure a reduction in the transmission of the virus. Models have demonstrated that in combination with routine mosquito control measures and the appropriate use of mosquitoicides, the transmission of Zika virus in the population can be effectively reduced.
- Zika virus,
- immigration,
- stability,
- screening tests,
- optimal control
Citation: Zongmin Yue, Yitong Li, Fauzi Mohamed Yusof. Dynamic analysis and optimal control of Zika virus transmission with immigration[J]. AIMS Mathematics, 2023, 8(9): 21893-21913. doi: 10.3934/math.20231116

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Abstract

In this paper, a type of Zika virus model with immigration is considered. Additionally based on the risk of infected immigrants, we propose a control measure of screening for immigrants and a three-measure control model of combined mosquito prevention and killing. The existence and stability of the equilibrium in the Zika virus model are analyzed. The necessary conditions for the existence of the optimal solution are given using Pontryagin's maximum principle. We focused on testing screening of the immigrating population to ensure a reduction in the transmission of the virus. Models have demonstrated that in combination with routine mosquito control measures and the appropriate use of mosquitoicides, the transmission of Zika virus in the population can be effectively reduced.

References

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