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The Complex Dynamics of Hepatitis B Infected Individuals with Optimal Control

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Abstract

This paper proposes various stages of the hepatitis B virus (HBV) besides its transmissibility and nonlinear incidence rate to develop an epidemic model. The authors plan the model, and then prove some basic results for the well-posedness in term of boundedness and positivity. Moreover, the authors find the threshold parameter R0, called the basic/effective reproductive number and carry out local sensitive analysis. Furthermore, the authors examine stability and hence condition for stability in terms of R0. By using sensitivity analysis, the authors formulate a control problem in order to eradicate HBV from the population and proved that the control problem actually exists. The complete characterization of the optimum system was achieved by using the 4th-order Runge-Kutta procedure.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China

    Anwarud Din & Yongjin Li

  2. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Murad Ali Shah

Authors
  1. Anwarud Din
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  2. Yongjin Li
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  3. Murad Ali Shah
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Corresponding author

Correspondence to Yongjin Li.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 11971493.

This paper was recommended for publication by Editor YOU Keyou.

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Cite this article

Din, A., Li, Y. & Shah, M.A. The Complex Dynamics of Hepatitis B Infected Individuals with Optimal Control. J Syst Sci Complex 34, 1301–1323 (2021). https://doi.org/10.1007/s11424-021-0053-0

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  • DOI: https://doi.org/10.1007/s11424-021-0053-0

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