A computational stochastic procedure for solving the epidemic breathing transmission system

Area of Science:

• Epidemiology
• Computational Mathematics
• Artificial Intelligence

Background:

• Breathing transmission epidemics pose significant public health challenges.
• Mathematical models are crucial for understanding and predicting epidemic dynamics.
• Nonlinear stiff ordinary differential equations often describe complex epidemic systems.

Purpose of the Study:

• To numerically simulate a nonlinear breathing transmission epidemic system.
• To propose and apply a novel stochastic scale conjugate gradient neural networks (SCGGNNs) procedure.
• To evaluate the accuracy and capability of the SCGGNNs for epidemic modeling.

Main Methods:

• Development of a mathematical model with four compartments: susceptible, exposed, infected, and recovered.
• Implementation of the stochastic scale conjugate gradient neural networks (SCGGNNs) with a log-sigmoid activation function and twenty hidden neurons.
• Numerical simulation of three distinct cases of the epidemic model using the SCGGNNs.
• Validation of the SCGGNNs accuracy by comparing results with database solutions and analyzing error metrics.

Main Results:

• The SCGGNNs achieved high precision with negligible absolute errors in the range of 10^-06 to 10^-07.
• Training, verification, and testing procedures successfully reduced the mean square error.
• The numerical simulations demonstrated the accuracy and capability of the SCGGNNs for the breathing transmission epidemic system.
• Error histograms, regression values, correlation tests, and state transitions confirmed the model's exactness.

Conclusions:

• The proposed stochastic SCGGNNs procedure is an effective and accurate method for simulating nonlinear breathing transmission epidemic systems.
• The SCGGNNs offer a reliable approach for epidemic forecasting and analysis.
• The study validates the robustness and precision of the SCGGNNs in handling complex mathematical models.