PDE Modelling of Population Dynamics using Physics Informed Neural Networks (PINNs)

Anthony Udo Akpan

In recent years, Artificial Intelligence (AI) has transformed scientific inquiry and technological innovation significantly in almost all facets of life. This paper presents a study of Physics-Informed Neural Networks (PINNs) solution techniques applied to Partial Differential Equation (PDE) models in population dynamics. Specifically, the paper focuses on modelling disease spread using an advection–diffusion– reaction partial differential equations (PDEs), with the solution sought through Physics-Informed Neural Networks (PINNs) technique. The community is being modelled as a bounded spatial domain where the disease density evolves over time and space. By embedding the underlying physical and biological laws into the network architecture, PINNs offer a robust and accurate framework to simulate infectious disease dynamics. Furthermore, numerical simulations, were implemented using the MATLAB ODE45 scheme, which provided insights into the interplay between disease progression, recovery, birth and death rate as parameter of interest in the transmission dynamics.

Keywords: PDE modelling, population dynamics, physics informed neural network,machine learning, biological laws, disease spread.

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