Artificial neural network-based approach for simulating influenza dynamics: A nonlinear SVEIR model with spatial diffusion

Abstract

Artificial Neural Networks (ANNs) have revolutionized machine learning by enabling systems to learn from data and generalize to new, unseen examples. As biologically inspired models, ANNs consist of interconnected neurons organized in layers, mimicking the human brain’s functioning. Their ability to model complex, nonlinear processes makes them powerful tools in various domains. In this study, the author apply ANNs to simulate the dynamics of a nonlinear Influenza transmission model with spatial diffusion. The model comprises five compartments: Susceptible ($S(x,t)$), Vaccinated ($V(x,t)$), Exposed ($E(x,t)$), Infected ($I(x,t)$), and Recovered ($R(x,t)$), governed by a system of partial differential equations (PDEs). We employ the Levenberg–Marquardt backpropagation algorithm to train the ANN, utilizing reference datasets generated through meshless and finite difference methods in MATLAB. The performance of the ANN is validated through mean square error (MSE) metrics, achieving a mean square error as low as $10^{-12}$. Regression and state transition plots illustrate the training, testing, and validation processes. Furthermore, absolute error analyses across various components of the system confirm the robustness and accuracy of the proposed approach. The data were split into 81% for training, with 9% each for testing and validation.