Given the critical role of time delays in epidemic modeling, this paper delves into the dynamics and finite-time optimal stabilization of a novel epidemic system characterized by such delays. Our findings reveal that time delays significantly influence both the system’s dynamics and the formulation of an optimal control strategy. Specifically, the system’s endemic equilibrium point remains locally asymptotically stable under mild conditions for small time delays. However, exceeding critical delay thresholds induces Hopf bifurcation. To closely regulate the system’s state towards the equilibrium point and minimize control costs, we propose an optimal control problem. We derive the explicit form of the optimal control strategy employing Pontryagin’s Maximum Principle. Finally, numerical simulations further confirm the theoretical results obtained in this paper.

中文翻译：

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时间延迟如何影响广义 SEAIR 模型的动力学和控制？


鉴于时间延迟在流行病建模中的关键作用，本文深入研究了以这种延迟为特征的新型流行病系统的动力学和有限时间最优稳定性。我们的研究结果表明，时间延迟显着影响系统的动力学和最优控制策略的制定。具体来说，系统的地方性平衡点在温和条件下在小时间延迟下保持局部渐近稳定。然而，超过临界延迟阈值会导致 Hopf 分岔。为了密切调节系统的状态接近平衡点并最小化控制成本，我们提出了最优控制问题。我们利用庞特里亚金极大值原理推导出最优控制策略的显式形式。最后，数值模拟进一步证实了本文获得的理论结果。