Solving an Infectious Disease Model considering Its Anatomical Variables with Stochastic Numerical Procedures

Area of Science:

• Mathematical modeling
• Computational biology
• Epidemiology

Background:

• Infectious disease dynamics are often modeled using prey-predator systems.
• Fractional-order models offer a more nuanced representation of complex biological processes.
• Numerical methods are crucial for solving these complex, nonlinear models.

Purpose of the Study:

• To numerically investigate an infectious disease using a nonlinear fractional-order prey-predator model.
• To implement and evaluate the efficacy of Levenberg-Marquardt backpropagation (LMB) based artificial neural networks (LMBNNs) for this model.
• To assess the model's three categories: susceptible, infected prey, and predator populations.

Main Methods:

• The study employed artificial neural networks (ANNs) integrated with the Levenberg-Marquardt backpropagation algorithm (LMBNNs).
• Data was partitioned for training (80%), validation (10%), and testing (10%).
• The LMBNNs approach was compared against the Adams-Bashforth-Moulton method.

Main Results:

• LMBNNs successfully solved the fractional prey-predator model for infectious disease dynamics.
• The method demonstrated a reduction in mean square error (M.S.E).
• Validation metrics including correlation, M.S.E, regression, and error histograms confirmed the model's accuracy and reliability.

Conclusions:

• LMBNNs provide an effective and accurate numerical solution for nonlinear fractional-order prey-predator models of infectious diseases.
• The proposed method shows high capability, consistency, and competence in simulating disease dynamics.
• This approach offers a robust tool for understanding and potentially controlling infectious disease spread.