Replacing the SIR epidemic model with a neural network and training it further to increase prediction accuracy

Abstract

Researchers often use theoretical models which provide a relatively sim- ple, yet concise and effective way of modelling various phenomena. However, it is a well-known fact that the more complex the model, the more complex the mathematical description is. For this reason, theoretical models generally avoid large complexity and aim for the simplest possible definition, which although makes models mathematically more manageable, in practice it also often leads to sub-optimal performance. Furthermore, the data collected during the observations usually contain confounding factors, for which a simple theoretical model can not be prepared. Overall, mathematical models are usually too rigid and sophisticated, and therefore cannot really deal with sudden changes in the environment. The application of artificial intelligence, however, provides a good opportunity to develop complex models that can combine the basic capabilities of the theoretical models with the ability to learn more complex relationships. It has been shown [16] that with neural networks, we can build such models that can approximate mathematical functions. Trained artificial neural networks are thus able to behave like theoretical models developed for different fields, while still retaining their overall flexibility, which guarantees an overall better performance in a complex realworld environment. The aim of our study is to show our notion that we can create an architecture using neural networks, which is able to approximate a given theoretical model, and then further improve it with the help of real data to suit the real world and its various aspects better. In order to validate the functionality of the architecture developed by us, we have selected a simple theoretical model, namely the Kermack-McKendrick one [4] as the base of our research. This is an SIR [2] model, which is a relatively simple compartmental epidemic model, based on differential equations that can be used well for infections that spread very similarly to influenza or COVID. However, on one hand, the SIR model relies too heavily on its parameters, with slight changes in them leading to drastic overall changes of the S, I and R curves, and on the other hand, the simplicity of the SIR model distorts its accuracy in many cases. In our paper, by using the SIR model, we will show that the architecture described above can be a valid approach to modeling the spread of a given disease (such as influenza or COVID-19). To this end, we detail the accuracy of our models with different settings and configurations and show that it performs better than both a simple mathematical model and a plain neural network with randomly initialized weights.