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Optimal control of an influenza model with mixed cross-infection by age group

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  • Chen, Ya
  • Zhang, Juping
  • Jin, Zhen

Abstract

Influenza is one of the major public health problems, and contact between all age groups and the emergence of influenza vaccines have played a vital role in the spread of influenza. In this paper, a mixed cross-infection influenza model by age group is established to study the effects of the number of contacts, vaccination rates, and protection rates among different age groups on the control of influenza transmission. The optimal control theory is applied to the model, the existence of the optimal control is proved, and the optimal path is obtained by using the Pontryagin’s maximum principle, by looking for the optimal control strategy to minimize the disease burden and intervention cost caused by influenza. Parameter estimation and numerical simulation are carried out using actual data, and the sensitivity analysis of the threshold R0 is carried out. The results show that compared with controlling the number of contacts between different age groups, increasing the vaccination rate and protection rate can reduce the number of infections to a greater extent. Finally, the gradient descent method is applied to numerical simulation of the optimal control strategy of the influenza model, and compared various control measures. We observe that considering the vaccination rate and protection rate is the best control strategy.

Suggested Citation

  • Chen, Ya & Zhang, Juping & Jin, Zhen, 2023. "Optimal control of an influenza model with mixed cross-infection by age group," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 410-436.
    • Handle: RePEc:eee:matcom:v:206:y:2023:i:c:p:410-436
    DOI: 10.1016/j.matcom.2022.11.019
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    References listed on IDEAS

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    1. Enayati, Shakiba & Özaltın, Osman Y., 2020. "Optimal influenza vaccine distribution with equity," European Journal of Operational Research, Elsevier, vol. 283(2), pages 714-725.
    2. Joël Mossong & Niel Hens & Mark Jit & Philippe Beutels & Kari Auranen & Rafael Mikolajczyk & Marco Massari & Stefania Salmaso & Gianpaolo Scalia Tomba & Jacco Wallinga & Janneke Heijne & Malgorzata Sa, 2008. "Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases," PLOS Medicine, Public Library of Science, vol. 5(3), pages 1-1, March.
    3. Zaman, Gul & Kang, Yong Han & Cho, Giphil & Jung, Il Hyo, 2017. "Optimal strategy of vaccination & treatment in an SIR epidemic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 63-77.
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    1. Fan, Yufei & Meng, Xueyu & Liu, Jun & Ma, Jun-Chao & Cai, Zhiqiang & Si, Shubin, 2025. "Hamiltonian optimal control of quarantine against epidemic spreading on complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).

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