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. 2021;34(4):1301-1323.
doi: 10.1007/s11424-021-0053-0. Epub 2021 Feb 4.

The Complex Dynamics of Hepatitis B Infected Individuals with Optimal Control

Anwarud Din  1 , Yongjin Li  1 , Murad Ali Shah  2
Affiliations

The Complex Dynamics of Hepatitis B Infected Individuals with Optimal Control

Anwarud Din et al. J Syst Sci Complex. 2021.

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 R 0, 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 R 0. 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.

Keywords: Hepatitis B epidemic model; non-linear incidence; normalized sensitivity index; numerical simulation; optimization theory; reproduction number; stability analysis.

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