Background and objective

an accurate estimation of the epidemiological model coefficients helps understand the basic principles of disease spreading. Some studies showed that dozens of hours are needed to simulate the traditional probabilistic cellular automaton (PCA) model, and dozens of hours are spent for a fine-tuning of the system. Here, we propose a deep learning-based surrogate model to mimic a PCA model to reduce the simulations' computational time, maintaining an equivalent precision in the estimates.

Method

we consider PCA models based on regular lattices of different sizes to generate training data sets varying the parameters related to individuals' movement in the lattice and the disease infectivity. These parameters are the input variables for training the surrogate model, and the outputs parameters to be fitted are the percentages of susceptible and infected individuals at the steady-state, the basic reproduction number R₀, the peak value and the peak instant of infected individuals, I(τ) and τ, respectively.

Results

The proposed surrogate model can predict all the output variables with a low relative error. The surrogate model's training time is independent of the size of the lattice, and the time for evaluating a solution by the surrogate model is low and independent of the lattice size.

Conclusions

The surrogate model provides a fast simulation time for a generic Susceptible-Infected-Removed (SIR) model in a PCA, which is helpful for tuning the model before final simulations, supporting the initial search for inverse problems of parameters estimation in SIR models and providing a satisfactory estimation of the output variables for large populations.

中文翻译：

---

基于深度学习的概率细胞自动机流行模型参数识别问题的替代模型

背景和目标

流行病学模型系数的准确估计有助于理解疾病传播的基本原理。一些研究表明，模拟传统的概率细胞自动机（PCA）模型需要数十个小时，而对系统进行微调则要花费数十个小时。在这里，我们提出了一个基于深度学习的替代模型来模仿PCA模型，以减少模拟的计算时间，并在估计中保持等效精度。

方法

我们考虑基于不同大小的规则晶格的PCA模型来生成训练数据集，这些数据集会改变与个体在晶格中的运动和疾病的传染性相关的参数。这些参数是用于训练替代模型的输入变量，要拟合的输出参数是稳态下易感和受感染个体的百分比，基本繁殖数R ₀，受感染个体的峰值和峰值瞬间，分别为I（τ）和τ。

结果

所提出的替代模型可以以较低的相对误差预测所有输出变量。替代模型的训练时间与晶格的大小无关，并且由替代模型评估解决方案的时间很短，并且与晶格的大小无关。

结论

替代模型为PCA中的通用易感性感染去除（SIR）模型提供了快速的仿真时间，这有助于在最终仿真之前调整模型，支持对SIR模型中参数估计的反问题进行初步搜索并提供对大量人口的输出变量进行令人满意的估计。