Optimal control analysis of hepatitis B virus with treatment and vaccination

Abstract

Hepatitis B infection is one of the global health problems and potentially life-threatening liver infection. This infection is preventable and can be controlled using vaccination and proper treatment. The mathematical modeling approach could be used effectively to study the dynamics and to present the appropriate control inventions of infectious diseases including hepatitis B infection. This paper presents the analysis of the Hepatitis B virus through a new mathematical model in the presence of treatment and vaccinations. We show that the model is stable asymptotically (locally and globally) at the disease-free case. Using the persistence analysis, we prove that the model is uniformly persistent if the threshold quantity is greater than unity. The global sensitivity of the threshold quantity is carried out in order to set appropriate control measures for infection minimization. In view of the sensitivity results, we formulate the control model using optimal control theory by considering three control variables. Considering of different controls combination, we introduce four different control strategies to minimize the spread of the hepatitis B infection in the population. Finally, to illustrate the effectiveness of each strategy for the eradication of infection, we perform and discuss the numerical simulations in detail.

Keywords

• Mathematical model
• Stability results
• Optimal control problem
• Persistent theory
• Numerical simulations