标题： 非线性流行病动力学的Koopman算子框架：应用于SIRSD模型 显示英文标题

标题： A Koopman Operator Framework for Nonlinear Epidemic Dynamics: Application to an SIRSD Model

摘要： 我们开发并分析了一个SIRSD流行病模型，该模型通过引入免疫减弱和疾病诱导的死亡率，扩展了经典的SIR框架。严格的适定性分析确保了解的存在性、唯一性、正性和有界性，保证了模型的流行病学可行性。为了促进理论研究和数据驱动建模，我们将系统重新表述为归一化变量。为了捕捉和预测复杂的非线性流行病动力学，我们使用了Koopman算子框架，结合扩展动态模式分解（EDMD）和一个流行病学启发的可观测量字典。我们比较了两种Koopman近似方法：一种基于最小流行病学字典，另一种则包含了非线性和交叉项。我们使用非标准有限差分（NSFD）方案生成了四种代表性流行病的合成数据：SARS-CoV-2、季节性流感、埃博拉和麻疹。数值实验表明，基于Koopman的方法能够有效识别主导的流行病模式，并准确预测关键的爆发特征，包括峰值感染动态。 显示英文摘要

摘要： We develop and analyze an SIRSD epidemic model, which extends the classical SIR framework by incorporating waning immunity and disease-induced mortality. A rigorous well-posedness analysis ensures the existence, uniqueness, positivity, and boundedness of solutions, guaranteeing the model's epidemiological feasibility. To facilitate theoretical investigations and data-driven modeling, we reformulated the system in normalized variables. To capture and predict complex nonlinear epidemic dynamics, we use the Koopman operator framework with extended dynamic mode decomposition (EDMD) and an epidemiologically informed dictionary of observables. We compare two Koopman approximations: one based on a minimal epidemiological dictionary and another enriched with nonlinear and cross terms. We generate synthetic data using a nonstandard finite difference (NSFD) scheme for four representative epidemics: SARS-CoV-2, seasonal influenza, Ebola, and measles. Numerical experiments demonstrate that the Koopman-based approach effectively identifies dominant epidemic modes and accurately predicts key outbreak characteristics, including peak infection dynamics.