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The Complex Dynamics of Hepatitis B Infected Individuals with Optimal Control

Authors
  • Din, Anwarud1
  • Li, Yongjin1
  • Shah, Murad Ali2
  • 1 Sun Yat-sen University,
  • 2 Beijing Normal University,
Type
Published Article
Journal
Journal of Systems Science and Complexity
Publisher
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Publication Date
Feb 04, 2021
Pages
1–23
Identifiers
DOI: 10.1007/s11424-021-0053-0
PMID: 33564220
PMCID: PMC7861011
Source
PubMed Central
Keywords
License
Unknown

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.

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