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Analysis and Optimal Control of a Two-Strain SEIR Epidemic Model with Saturated Treatment Rate

Author

Listed:
  • Yudie Hu

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China)

  • Hongyan Wang

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China)

  • Shaoping Jiang

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, China)

Abstract

In this paper, we conducted a study on the optimal control problem of an epidemic model which consists of two strain with different types of incidence rates: bilinear and non-monotonic. We also considered use of the saturation treatment function. Two basic regeneration numbers are calculated from the epidemic model, which are denoted as R 1 and R 2 . The global stability of the disease-free equilibrium point was studied by the Lyapunov method, and it was proved that the disease-free equilibrium point is globally asymptotically stable when R 1 and R 2 are less than one. Finally, we formulated a time-dependent optimal control problem by Pontryagin’s maximum principle. Numerical simulations were performed to establish the effects of model parameters for disease transmission as well as the effects of control.

Suggested Citation

  • Yudie Hu & Hongyan Wang & Shaoping Jiang, 2024. "Analysis and Optimal Control of a Two-Strain SEIR Epidemic Model with Saturated Treatment Rate," Mathematics, MDPI, vol. 12(19), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3026-:d:1487745
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    References listed on IDEAS

    as
    1. Khan, Muhammad Altaf & Khan, Yasir & Islam, Saeed, 2018. "Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 210-227.
    2. Hailay Weldegiorgis Berhe & Oluwole Daniel Makinde & David Mwangi Theuri, 2019. "Parameter Estimation and Sensitivity Analysis of Dysentery Diarrhea Epidemic Model," Journal of Applied Mathematics, Hindawi, vol. 2019, pages 1-13, February.
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