The susceptible-infected-recovered (SIR) model has greatly evidenced epidemiology despite its apparent simplicity. Most applications of the SIR framework use a form of nonlinear incidence to describe the number of new cases per instant. We adapt theorems to analyze the stability of SIR models with a generalized nonlinear incidence structure. These theorems are then applied to the case of standard incidence and incidence resulting from adaptive behavioral response based on epidemiological-economic theory. When adaptive behavior is included in the SIR model multiple equilibria and oscillatory epidemiological dynamics can occur over a greater parameter space. Our analysis, based on the epidemiological-economic incidence, provides new insights into epidemics as complex adaptive systems, highlights important nonlinearities that lead to complex behavior, and provides mechanistic motivation for a shift away from standard incidence, and outlines important areas of research related to the complex-adaptive dynamics of epidemics.

中文翻译：

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SIR Dynamics 与经济驱动的联系率

易感-感染-恢复 (SIR) 模型尽管表面上很简单，但已极大地证明了流行病学。SIR 框架的大多数应用程序使用一种非线性关联形式来描述每瞬间的新病例数。我们采用定理来分析具有广义非线性入射结构的 SIR 模型的稳定性。然后将这些定理应用于标准发病率和基于流行病学经济理论的适应性行为反应引起的发病率的情况。当适应性行为包含在 SIR 模型中时，多个平衡和振荡的流行病学动态可以在更大的参数空间上发生。我们的分析基于流行病学-经济发生率，提供了对作为复杂适应系统的流行病的新见解，突出了导致复杂行为的重要非线性，