SEINN: A deep learning algorithm for the stochastic epidemic model

Thomas Torku; Abdul Khaliq; Fathalla Rihan; Thomas Torku; Abdul Khaliq; Fathalla Rihan

doi:10.3934/mbe.2023729

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 9: 16330-16361. doi: 10.3934/mbe.2023729

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SEINN: A deep learning algorithm for the stochastic epidemic model

1.
University Studies Department, Middle Tennessee State University, Murfreesboro, TN 37132, USA
2.
Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA
3.
Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, Abu Dhabi, UAE

Academic Editor: Shangce Gao

Received: 16 May 2023 Revised: 04 July 2023 Accepted: 09 July 2023 Published: 14 August 2023

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.
- deep learning,
- data-driven,
- stochastic differential equation,
- regularization,
- stochastic epidemiology informed neural network,
- computational analysis,
- nonlinear incidence rate
Citation: Thomas Torku, Abdul Khaliq, Fathalla Rihan. SEINN: A deep learning algorithm for the stochastic epidemic model[J]. Mathematical Biosciences and Engineering, 2023, 20(9): 16330-16361. doi: 10.3934/mbe.2023729

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Abstract

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.

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