The effect of environmental load and various types of noises on the dynamics of hepatitis B virus transmission

Le résumé fourni par la source

Hepatitis B is one of the most contagious diseases, affecting more than two billion people worldwide. Various real-world uncertainties and irregularities can influence the transmission and progression of hepatitis B virus (HBV). For example, environmental and behavioral factors, seasonal migration, long-term healthcare accessibility, delayed behavioral responses to public health campaigns, and mass vaccination failures, as well as migration influxes, natural disasters, or the breakdown of healthcare systems, are the main factors that significantly influence the transmission of HBV. Modeling the dynamics of HBV with appropriate structure and assumptions is not only important to show the current disease scenario but also helpful for future forecasting of its dynamics. In this work, we develop a stochastic epidemic model for HBV transmission that incorporates stochastic perturbations: white noise, colored noise, and Lévy noise to study the rapid fluctuations in transmission or recovery rates, seasonal or policy driven changes in transmission patterns and the impact of rare but significant events, such as mass migrations, sudden outbreaks, or abrupt changes in public health responses. We rigorously analyze the well-posedness of the model by proving the existence, uniqueness, and positivity of global solutions. We derive the basic reproductive number and establish threshold conditions for disease extinction and persistence in the stochastic setting. Finally, extensive numerical simulations are carried out to validate the theoretical results and illustrate the dynamics of the model.

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