The Complex Dynamics of Hepatitis B Infected Individuals with Optimal Control

• Published in: Journal of systems science and complexity Vol. 34; no. 4; pp. 1301 - 1323
• Main Authors: Din, Anwarud, Li, Yongjin, Shah, Murad Ali
• Format: Journal Article
• Language: English
• Published: Beijing Academy of Mathematics and Systems Science, Chinese Academy of Sciences 01.08.2021; Springer Nature B.V
• Subjects: Complex Systems; Control; Hepatitis B; Mathematics; Mathematics and Statistics; Mathematics of Computing; Operations Research/Decision Theory; Optimal control; Optimization; Runge-Kutta method; Sensitivity analysis; Stability analysis; Statistics; Systems Theory; reproduction number; Hepatitis B epidemic model; non-linear incidence; stability analysis; normalized sensitivity index; optimization theory; numerical simulation
• ISSN: 1009-6124; 1559-7067
• DOI: 10.1007/s11424-021-0053-0

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 4 th -order Runge-Kutta procedure.