Mathematical Model of Hepatitis B Disease with Optimal Control and Cost-Effectiveness Analysis

Abstract

In this paper, a mathematical model of hepatitis B disease with a two-dose vaccine series has been formulated and analyzed. We demonstrated that the model’s disease-free equilibrium is globally asymptotically stable when the basic reproduction number $\left(R_0\right)$ is less than one, whereas the model’s endemic equilibrium is locally asymptotically stable when $R_0$ is greater than one. Sensitivity analysis is performed, and based on its results, the model is extended to an optimal control problem by incorporating two control interventions, namely, prevention and enhanced newborn vaccination. Finally, simulation analyses of the model are conducted to illustrate the theoretical findings and effectiveness of each strategy, which indicates that the use of prevention efforts is the most cost-saving strategy.