Modelling the dynamics of acute and chronic hepatitis B with optimal control

Tahir Khan, Fathalla A. Rihan, Hijaz Ahmad

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


This article examines hepatitis B dynamics under distinct infection phases and multiple transmissions. We formulate the epidemic problem based on the characteristics of the disease. It is shown that the epidemiological model is mathematically and biologically meaningful of its well-posedness (positivity, boundedness, and biologically feasible region). The reproductive number is then calculated to find the equilibria and the stability analysis of the epidemic model is performed. A backward bifurcation is also investigated in the proposed epidemic problem. With the help of two control measures (treatment and vaccination), we develop control strategies to minimize the infected population (acute and chronic). To solve the proposed control problem, we utilize Pontryagin’s Maximum Principle. Some simulations are conducted to illustrate the investigation of the analytical work and the effect of control analysis.

Original languageEnglish
Article number14980
JournalScientific reports
Issue number1
Publication statusPublished - Dec 2023

ASJC Scopus subject areas

  • General


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