Hepatitis B virus (HBV) is a significant health hazard in the world. This article describes a new mathematical model, which takes into account three intervention measures: education, vaccination, and therapy. The main novelty of our method is that we introduce two new compartments, an initially recovered population \(I_i(k)\) ,which counts persons with provisional immunity, and a class of reinfected \(R_i(k)\) ,of the source of immunity lost and of re-entry into the infectious pool. This framework explicitly models the clinically important interactions of waning immunity and vaccine failure using a more biologically realistic model than earlier ones which assume permanent recovery. We prove the well-posedness of the model by showing the positivity, boundedness, and stability of solutions, and obtain the basic reproduction number. \(R_0^{HBV}\) applying the next-generation approach. The main aim of the given research is to develop and identify an optimal control strategy that will identify the best combination of these three interventions. We develop an optimal control model that reduces the prevalence of the infection and the costs of the intervention. Numerical modeling shows that, although each intervention has a medium effect, the most meaningful decrease in HBV prevalence occurs when the two are combined. Our results offer a sound theoretical basis to the policy of health promotion, emphasizing that the combination of multiple strategies is significantly more effective than a single one in attaining long-term control and potentially eliminating HBV.
