A stochastic SACR epidemic model for HBV transmission

Area of Science:

• Epidemiology
• Mathematical Biology
• Stochastic Processes

Background:

• Hepatitis B poses a significant global health challenge.
• Understanding disease dynamics requires robust mathematical models.
• Environmental factors can influence disease transmission.

Purpose of the Study:

• To develop a stochastic model for hepatitis B incorporating environmental fluctuations.
• To analyze the impact of white noise on hepatitis B transmission dynamics.
• To determine conditions for disease extinction and persistence.

Main Methods:

• Development of a stochastic Severe Acute Cholangitis and Renal Syndrome (SACR) hepatitis B epidemic model.
• Application of stochastic Lyapunov function theory for analyzing model solutions.
• Derivation of conditions for disease extinction and persistence.
• Numerical simulations using a first-order Itô-Taylor stochastic scheme.

Main Results:

• Existence and uniqueness of a global positive solution were proven.
• Sufficient conditions for the extinction and persistence of hepatitis B were established.
• Theoretical results were validated through numerical simulations.

Conclusions:

• The stochastic model provides insights into hepatitis B dynamics under environmental fluctuations.
• The study offers a framework for understanding disease persistence and extinction.
• Numerical simulations confirm the theoretical findings, enhancing model reliability.