Application of neural-network hybrid models in estimating the infection functions of nonlinear epidemic models

TL;DR

This paper introduces a hybrid neural network approach combined with bifurcation theory and a novel loss function to accurately estimate infection functions in nonlinear epidemic models, demonstrated on COVID-19 data.

Contribution

It presents a new hybrid nonlinear epidemic neural network model with a specialized loss function and theoretical conditions for estimating infection functions in nonlinear epidemic models.

Findings

Successfully predicts infection functions in nonlinear epidemic models.

Accurately captures COVID-19 infectivity changes.

Verifies model robustness through numerical experiments.

Abstract

Hybrid neural network models combine the advantages of a neural network's fitting functionality with differential equation models to reflect actual physical processes and are widely used in analyzing time-series data. Most related studies have focused on linear hybrid models, but only a few have examined nonlinear problems. In this work, we use a hybrid nonlinear epidemic neural network as the entry point to study its power in predicting the correct infection function of an epidemic model. To achieve this goal, we combine the bifurcation theory of the nonlinear differential model with the mean-squared error loss and design a novel loss function to ensure model trainability. Furthermore, we find the unique existence conditions supporting ordinary differential equations to estimate the correct infection function. Using the Runge Kutta method, we perform numerical experiments on our proposed model and verify its soundness. We also apply it to real COVID-19 data to accurately discover the change law of its infectivity.