Neural ordinary differential equations for parameter estimation, simulation and forecasting of infectious disease dynamics: Applications to HIV/AIDS and malaria models

Abstract

This study investigates the application of Neural Ordinary Differential Equations (Neural ODEs) for the simulation and parameter estimation of disease models. The primary objective is to simulate disease dynamics and forecast future transmission trends using a trained Neural ODE framework. The model adopts a numerically informed and data-driven approach that integrates epidemiological datasets with disease-informed neural networks to capture transmission behaviour. For HIV/AIDS, transmission dynamics are generated using synthetic datasets obtained via the fourth-order Runge-Kutta method, whereas predictions for malaria are based on real-world epidemiological data. The results demonstrate that the Neural ODE framework effectively learns disease transmission patterns, accurately captures the progression of compartmental dynamics, estimates key epidemiological parameters, and produces reliable forecasts from both observed and numerically generated data. It is observed that increasing the number of training epochs improves predictive performance, as the model better captures complex nonlinear patterns and fluctuations within disease compartments. However, a notable limitation is that higher epoch counts substantially increase computational time, with training durations extending to several hours.