We consider a generic Susceptible–Infected–Recovered–Hospitalized–Deceased model for the spread of infectious diseases over contact networks. Precisely, the deceased compartment tracks the cumulative number of deaths that are not offset by births. After properly reducing the model to a nonlinear susceptible–infected–recovered (SIR) model on a graph, we systematically investigate its invariant sets, its stability, convergence, monotonicity and equilibrium properties. Given the significant influence of network structure on infection dynamics, the basic reproduction number is insufficient for predicting disease evolution. We introduce more suitable threshold conditions for the model. However, due to the inherent high dimensionality of networks, modelling transmission through them necessitates numerical methods. This work provides numerical demonstrations of epidemic spread, validating the derived threshold conditions. Additionally, we highlight the limitations of social distancing measures in the presence of stable equilibria with a persistent infected population using especially machine learning tools.

中文翻译：

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网络流行病模型：从数学分析到机器学习实验


我们考虑了一种通用的易感 - 感染 - 康复 - 住院 - 已故模型，用于传染病在接触网络上的传播。准确地说，已故区间跟踪未被出生数抵消的累计死亡人数。在图上将模型适当简化为非线性易感-感染-恢复 （SIR） 模型后，我们系统地研究了它的不变集、稳定性、收敛性、单调性和平衡性质。鉴于网络结构对感染动力学的显著影响，基本繁殖数不足以预测疾病演变。我们为模型引入了更合适的阈值条件。然而，由于网络固有的高维性，通过它们对传输进行建模需要数值方法。这项工作提供了流行病传播的数值演示，验证了推导的阈值条件。此外，我们强调了在与持续感染人群保持稳定平衡的情况下，特别是使用机器学习工具时，社交距离措施的局限性。