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<p>In this work, we develop a stochastic SEIS epidemic model that accounts for nonlinear innate immunity and media awareness. We begin by establishing the well-posedness of the model, ensuring the existence of positive solutions. We then derive sufficient conditions for disease extinction and for persistence in mean. Using Khasminskii’s theory, we identify criteria for the existence of a unique ergodic stationary distribution. An optimal control problem is subsequently analyzed using Pontryagin’s maximum principle, enabling the simultaneous minimization of disease burden and intervention costs while defining effective strategies to limit disease spread. The results highlight the significant influence of stochastic perturbations on the model’s dynamics, revealing notable differences compared to the corresponding deterministic model, and confirm the cost-effectiveness and the importance of the optimal control strategy. Finally, numerical simulations are provided to illustrate the theoretical findings.</p>

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Stochastic optimal control of treatment for an epidemic model incorporating nonlinear innate immunity and media awareness

  • 期刊论文

  • 发表日期：

    2026年7月11日

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  • Abdelatif Karimine,
  • Mohammed Lakhal,
  • Regragui Taki,
  • Zuhair Bahraoui

摘要

In this work, we develop a stochastic SEIS epidemic model that accounts for nonlinear innate immunity and media awareness. We begin by establishing the well-posedness of the model, ensuring the existence of positive solutions. We then derive sufficient conditions for disease extinction and for persistence in mean. Using Khasminskii’s theory, we identify criteria for the existence of a unique ergodic stationary distribution. An optimal control problem is subsequently analyzed using Pontryagin’s maximum principle, enabling the simultaneous minimization of disease burden and intervention costs while defining effective strategies to limit disease spread. The results highlight the significant influence of stochastic perturbations on the model’s dynamics, revealing notable differences compared to the corresponding deterministic model, and confirm the cost-effectiveness and the importance of the optimal control strategy. Finally, numerical simulations are provided to illustrate the theoretical findings.