Stochastic analysis and control for a delayed Hepatitis B epidemic model

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.

Keywords:

• Stochastic analysis
• optimal control
• time-delay
• Hepatitis B epidemic model

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work is supported by Natural Science Foundation of China grants (12261028, 11761025, 11961018), the Hainan Province Science and Technology Special Fund (ZDYF2021SHFZ231), Natural Science Foundation of Hainan Province (120RC451, 2019RC168), Hainan Province Innovative Scientific Research Project for Graduate Students (Qhys2021-208), the specific research fund of The Innovation Platform for Academicians of Hainan Province.

Notes on contributors

Jingwen Zhang

Jingwen Zhang: proposed and designed this study and did numerical simulations. Zhigang Wang: proposed methodology. Yan Wang: analyzed data. Haohua Wang: proposed and designed this study and wrote the manuscript.

Zhigang Wang

Jingwen Zhang: proposed and designed this study and did numerical simulations. Zhigang Wang: proposed methodology. Yan Wang: analyzed data. Haohua Wang: proposed and designed this study and wrote the manuscript.

Yan Wang

Jingwen Zhang: proposed and designed this study and did numerical simulations. Zhigang Wang: proposed methodology. Yan Wang: analyzed data. Haohua Wang: proposed and designed this study and wrote the manuscript.

Haohua Wang

Jingwen Zhang: proposed and designed this study and did numerical simulations. Zhigang Wang: proposed methodology. Yan Wang: analyzed data. Haohua Wang: proposed and designed this study and wrote the manuscript.