Stochastic optimal control analysis for HBV epidemic model with vaccination

Abstract

Several classes are discussed in this paper, including susceptibles, vaccinates, acutes, chronics, hospitalized, and recovered. In terms of dynamic behaviour, the model provides a substantial description of Hepatitis B. Hepatitis B transmission dynamics and infection risk can be predicted using the model. A vaccine strategy or intervention can also be identified using it. Given the initial positive data, the model possesses a bounded, unique, and positive solution. Furthermore, we have established the model's stability through the application of stochastic Lyapunov functional theory. The examination of an infection's stationary distribution and potential extinction is conducted under specific conditions. Both stochastic and deterministic control problems were scrutinized, with optimal control theory employed to manage the external control measures for the disease's containment. The analytical findings have been elucidated through graphical representations.

Dynamics of Hepatitis B Virus Transmission with a Lévy Process and Vaccination Effects

“…Based on the dynamic features of HBV, Murad et al [27] formulated a stochastic epidemic model for the disease and presented a model analysis under the vaccination effect. In this work, we will extend the model presented in [27], focusing on partial immunity, the nonlinear incidence of the infection, and vaccination as a control compartment.…”

“…Based on the dynamic features of HBV, Murad et al [27] formulated a stochastic epidemic model for the disease and presented a model analysis under the vaccination effect. In this work, we will extend the model presented in [27], focusing on partial immunity, the nonlinear incidence of the infection, and vaccination as a control compartment. To formulate the model, we will decompose the entire population into six compartments: the susceptibles S(t), acute infections I 1 (t), chronically infected people I 2 (t), the hospitalized class H(t), the immune group R(t), and vaccinated individuals V(t).…”