Stochastic analysis and control for a delayed Hepatitis B epidemic model

Jingwen Zhang, Zhigang Wang, Yan Wang and Haohua Wang

Computer Methods in Biomechanics and Biomedical Engineering, 2024, vol. 27, issue 6, 700-716

Abstract: Considering the time delay originating from a certain incubation period or asymptomatic state, we propose a delayed epidemic system within the noisy environment of the hepatitis B virus to analyze the mechanism of disease transmission and elucidate how to control it by applying the strategy of vaccinating and treatment. Applying stochastic Lyapunov functional theory, we first construct an integral Lyapunov function coupling the time delay and stochastic fluctuation to investigate whether there exists a unique global solution to the model. Next, we yield the threshold condition for controlling disease extinction, and persistence, as well as its stationary distribution. Governed by these sufficient conditions, we study the existence of optimal control solutions in deterministic and stochastic scenarios to uncover how to accelerate disease extinction through vaccination and treatment. The results indicate that the time delay will prolong the duration of the disease for the original system but suppress the peak value of HBV in the controlled system. Finally, we verify the versatility of theoretical results by numerical simulations. These results will effectively decipher the importance of the time delay in the control of hepatitis B.

Date: 2024
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DOI: 10.1080/10255842.2023.2199900

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