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The Complex Dynamics of Hepatitis B Infected Individuals with Optimal Control

  

  1. DIN Anwarud · LI Yongjin (Corresponding author)
    Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China.
    Email: anwarud@mail.sysu.edu.cn; stslyj@mail.sysu.edu.cn.
    SHAH Murad Ali
    School of Mathematical Sciences; Beijing Normal University, Beijing 100875, China.
    Email: muradmath@yahoo.com.
  • Online:2021-08-25 Published:2021-08-10

DIN Anwarud · LI Yongjin · SHAH Murad Ali. The Complex Dynamics of Hepatitis B Infected Individuals with Optimal Control[J]. Journal of Systems Science and Complexity, 2021, 34(4): 1301-1323.

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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