Since infectious pathogens start spreading into a susceptible population, mathematical models can provide policy makers with reliable forecasts and scenario analyses, which can be concretely implemented or solely consulted. In these complex epidemiological scenarios, machine learning architectures can play an important role, since they directly reconstruct data-driven models circumventing the specific modelling choices and the parameter calibration, typical of classical compartmental models. In this work, we discuss the efficacy of Kernel Operator Learning (KOL) to reconstruct population dynamics during epidemic outbreaks, where the transmission rate is ruled by an input strategy. In particular, we introduce two surrogate models, named KOL-m and KOL-$\partial$, which reconstruct in two different ways the evolution of the epidemics. Moreover, we evaluate the generalization performances of the two approaches with different kernels, including the Neural Tangent Kernels, and compare them with a classical neural network model learning method. Employing synthetic but semi-realistic data, we show how the two introduced approaches are suitable for realizing fast and robust forecasts and scenario analyses, and how these approaches are competitive for determining optimal intervention strategies with respect to specific performance measures.

翻译：自传染性病原体开始在易感人群中传播以来，数学模型可为政策制定者提供可靠的预测和情景分析，这些分析既可实际实施也可仅作参考。在这些复杂的流行病学场景中，机器学习架构可发挥重要作用，因其能直接重构数据驱动模型，规避经典仓室模型中特有的建模选择与参数校准过程。本研究探讨了核算子学习在流行病爆发期间重构种群动态的有效性，其中传播速率受输入策略调控。具体而言，我们引入两种替代模型——KOL-m和KOL-$\partial$——它们以不同方式重构流行病演化过程。此外，我们评估了两种方法在不同核函数（包括神经正切核）下的泛化性能，并与经典神经网络模型学习方法进行对比。通过使用合成但半真实的数据，我们展示了这两种方法如何适用于实现快速鲁棒的预测与情景分析，以及如何针对特定性能指标确定最优干预策略。