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Optimal Control of Mitigation Strategies for Dengue Virus Transmission

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Abstract

Dengue virus is transmitted by Aedes mosquitoes, posing threat to people’s health and leading to great economic cost in many tropical and subtropical regions. We develop an ordinary differential equation model taking into account multiple strains of dengue virus. Using the model, we assess the effectiveness of human vaccination considering its waning and failure. We derive the lower bound and upper bound for the final size of the epidemic. Sensitivity analysis quantifies the impact of parameters on the basic reproduction number. Different scenarios of vaccinating humans show that it is better to vaccinate humans at early stages. We find that the cumulative number of infected humans is small when the vaccination rate is high or the waning rate is low for previously infected humans. We analyze the necessary conditions for implementing optimal control and derive the corresponding optimal solutions for mitigation dengue virus transmission by applying Pontryagin’s Maximum Principle. Our findings may provide guidance for the public health authorities to implement human vaccination and other mitigation strategies.

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Acknowledgements

Ling Xue is funded by National Natural Science Foundation of China 11501145, the Fundamental Research funds for the Central Universities of China 3072020CFT2402. Wei Sun is funded by the Fundamental Research funds for the Central Universities of China, and National Science Foundation for Young Scholars of Heilongjiang Province QC2018004.

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Authors and Affiliations

  1. College of Automation, Harbin Engineering University, Harbin, 150001, China

    Ling Xue & Xue Ren

  2. College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, China

    Ling Xue, Xue Ren & Wei Sun

  3. Department of Mathematics and Statistics, Queen’s University, Kingston, K7L 3N6, Canada

    Felicia Magpantay

  4. Department of Mathematics and Statistics, York University, Toronto, M3J 1P3, Canada

    Huaiping Zhu

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  1. Ling Xue
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Correspondence to Wei Sun.

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Xue, L., Ren, X., Magpantay, F. et al. Optimal Control of Mitigation Strategies for Dengue Virus Transmission. Bull Math Biol 83, 8 (2021). https://doi.org/10.1007/s11538-020-00839-3

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