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<p>In this paper, a stochastic HBV/HCV model with Lévy jumps, distributed delays and nonlinear incidence is proposed. By the linear chain technique, we convert the stochastic model in the case of weak kernel into a nine-dimensional degenerate stochastic system. The high dimensionality of the system significantly increases the computational complexity, particularly in the construction of Lyapunov functions. Through rigorous theoretical analysis, we investigate the rich dynamical behaviors of the system. Firstly, we prove that there exists a unique global positive solution for any positive initial value of the stochastic system. Then, by constructing some appropriate Lyapunov functions, we establish the sufficient conditions for the extinction and persistence in the mean of the disease. Furthermore, the asymptotic behaviors around the disease-free equilibrium and endemic equilibrium are studied. Finally, numerical simulations are conducted to verify the theoretical results.</p>

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Dynamics of a general stochastic HBV/HCV model with Lévy jumps and distributed delays

  • 期刊论文

  • 发表日期：

    2026年2月25日

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  • Yihan Zhang,
  • Qiaoling Chen,
  • Sanyi Tang,
  • Zhidong Teng

摘要

In this paper, a stochastic HBV/HCV model with Lévy jumps, distributed delays and nonlinear incidence is proposed. By the linear chain technique, we convert the stochastic model in the case of weak kernel into a nine-dimensional degenerate stochastic system. The high dimensionality of the system significantly increases the computational complexity, particularly in the construction of Lyapunov functions. Through rigorous theoretical analysis, we investigate the rich dynamical behaviors of the system. Firstly, we prove that there exists a unique global positive solution for any positive initial value of the stochastic system. Then, by constructing some appropriate Lyapunov functions, we establish the sufficient conditions for the extinction and persistence in the mean of the disease. Furthermore, the asymptotic behaviors around the disease-free equilibrium and endemic equilibrium are studied. Finally, numerical simulations are conducted to verify the theoretical results.