Exact solutions of epidemic models are critical for identifying the severity and mitigation possibility for epidemics. However, solving complex models can be difficult when interfering conditions from the real-world are incorporated into the models. In this paper, we focus on the generally unsolvable adaptive susceptible-infected-susceptible (ASIS) epidemic model, a typical example of a class of epidemic models that characterize the complex interplays between the virus spread and network structural evolution. We propose two methods based on mean-field approximation, i.e., the first-order mean-field approximation (FOMFA) and higher-order mean-field approximation (HOMFA), to derive the exact solutions to ASIS models. Both methods demonstrate the capability of accurately approximating the metastable-state statistics of the model, such as the infection fraction and network density, with low computational cost. These methods are potentially powerful tools in understanding, mitigating, and controlling disease outbreaks and infodemics.

中文翻译：

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有限尺寸网络中自适应敏感感染敏感模型的高阶均值近似

流行病模型的精确解决方案对于识别流行病的严重性和缓解可能性至关重要。但是，当将来自现实世界的干扰条件合并到模型中时，很难求解复杂的模型。在本文中，我们将重点放在一般无法解决的自适应易感性感染易感性（ASIS）流行病模型上，这是一类流行病模型的典型示例，这些模型描述了病毒传播与网络结构演变之间的复杂相互作用。我们提出两种基于平均场近似的方法，即一阶平均场近似（FOMFA）和高阶平均场近似（HOMFA），以得出ASIS模型的精确解。两种方法都证明了能够精确逼近模型的亚稳态统计量，例如感染率和网络密度，计算成本低。这些方法可能是了解，缓解和控制疾病暴发和信息传播的潜在强大工具。