Stochastic modeling predicts various outcomes from stochasticity in the data, parameters and dynamical system. Stochastic models are deemed more appropriate than deterministic models accounting in terms of essential and practical information about a system. The objective of the current investigation is to address the issue above through the development of a novel deep neural network referred to as a stochastic epidemiology-informed neural network. This network learns knowledge about the parameters and dynamics of a stochastic epidemic vaccine model. Our analysis centers on examining the nonlinear incidence rate of the model from the perspective of the combined effects of vaccination and stochasticity. Based on empirical evidence, stochastic models offer a more comprehensive understanding than deterministic models, mainly when we use error metrics. The findings of our study indicate that a decrease in randomness and an increase in vaccination rates are associated with a better prediction of nonlinear incidence rates. Adopting a nonlinear incidence rate enables a more comprehensive representation of the complexities of transmitting diseases. The computational analysis of the proposed method, focusing on sensitivity analysis and overfitting analysis, shows that the proposed method is efficient. Our research aims to guide policymakers on the effects of stochasticity in epidemic models, thereby aiding the development of effective vaccination and mitigation policies. Several case studies have been conducted on nonlinear incidence rates using data from Tennessee, USA.

中文翻译：

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SEINN：随机流行病模型的深度学习算法。

随机建模根据数据、参数和动力系统的随机性预测各种结果。就系统的基本和实用信息而言，随机模型被认为比确定性模型更合适。当前研究的目标是通过开发一种新型深度神经网络（称为随机流行病学信息神经网络）来解决上述问题。该网络学习有关随机流行病疫苗模型的参数和动态的知识。我们的分析重点是从疫苗接种和随机性的综合影响的角度来检查模型的非线性发生率。基于经验证据，随机模型比确定性模型提供了更全面的理解，主要是当我们使用误差指标时。我们的研究结果表明，随机性的降低和疫苗接种率的提高与非线性发病率的更好预测相关。采用非线性发病率可以更全面地表示传播疾病的复杂性。对所提出方法的计算分析，重点是敏感性分析和过拟合分析，表明该方法是有效的。我们的研究旨在指导决策者了解流行病模型中随机性的影响，从而帮助制定有效的疫苗接种和缓解政策。使用美国田纳西州的数据对非线性发生率进行了几个案例研究。