Dynamic behavior and control of HBV model within stochastic information intervention

Abstract

The stochastic fluctuation of information induces the dynamic behavior and disease control strategy to change in the HBV epidemic model, but how stochastic information dissemination affects them is vague. Here, we consider an HBV epidemic model with stochastic information intervention. Using the Lyapunov function, we demonstrate that the system has a unique global positive solution, in addition, we also derive the threshold dynamics to obtain sufficient conditions that can ensure the extinction and persistence, as well as stationarity of the system. Moreover, we qualify the impact of stochasticity of the information on the optimal control strategy of the HBV, indicating that while information intervention could effectively reduce the disease peak, the fluctuation will attenuate this effect, i.e., the stable information is better than the noisy one. Finally, various stochastic and optimal control simulations are performed to verify the theoretical results and verify that optimal control can accelerate the extinction of the disease.

Keywords

• HBV model
• Information intervention
• Stochastic analysis
• Stationary distribution
• Optimal control