Department of Applied Mathematics, University of Waterloo, Waterloo, Canada.
Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada.
Bull Math Biol. 2023 Jun 19;85(8):71. doi: 10.1007/s11538-023-01174-z.
Predicting the evolution of diseases is challenging, especially when the data availability is scarce and incomplete. The most popular tools for modelling and predicting infectious disease epidemics are compartmental models. They stratify the population into compartments according to health status and model the dynamics of these compartments using dynamical systems. However, these predefined systems may not capture the true dynamics of the epidemic due to the complexity of the disease transmission and human interactions. In order to overcome this drawback, we propose Sparsity and Delay Embedding based Forecasting (SPADE4) for predicting epidemics. SPADE4 predicts the future trajectory of an observable variable without the knowledge of the other variables or the underlying system. We use random features model with sparse regression to handle the data scarcity issue and employ Takens' delay embedding theorem to capture the nature of the underlying system from the observed variable. We show that our approach outperforms compartmental models when applied to both simulated and real data.
预测疾病的演变具有挑战性，特别是在数据稀缺和不完整的情况下。用于模拟和预测传染病流行的最流行的工具是房室模型。它们根据健康状况将人群划分为不同的隔室，并使用动力系统对这些隔室的动态进行建模。然而，由于疾病传播和人类相互作用的复杂性，这些预定义的系统可能无法捕捉到疫情的真实动态。为了克服这一缺陷，我们提出了基于稀疏性和延迟嵌入的预测（SPADE4）方法来预测疫情。SPADE4 在不了解其他变量或底层系统的情况下预测可观察变量的未来轨迹。我们使用具有稀疏回归的随机特征模型来处理数据稀缺问题，并采用 Takens 的延迟嵌入定理从观测变量中捕获底层系统的性质。我们表明，当应用于模拟和真实数据时，我们的方法优于房室模型。
