On the neural network solutions of some mathematical epidemiology models

Objective: This study was carried out with the aim of developing an artificial neural network model that will predict the rate of positive cases, infected and recovered individuals in the population with respect to the COVID-19 pandemic in Turkey. Material and Methods: The study is carried out Turkey between November 2020 and May 2021 using confirmed COVID-19 data announced on the Ministry of Health website. The normalized data is used in the training of multilayer perceptron and residual artificial neural networks that produce numerical solutions in a way that converges to some mathematical epidemic models presented in the literature. The Mesh Adaptive Direct Search Method, which is a derivative-free optimization approach, is used to determine the weights of the neural network. Results: It has been observed that the artificial neural networks developed in the research are compatible with both the SI (Suspectible - Infected) and SIS (Suspectible - Infected - Suspectible) epidemic models and the real data observed. However, it was not possible to obtain the same finding for the SIR (Suspectible - Infected - Recovered) model. It was concluded that the main reason for this was the sudden and large change rates seen from time to time in the number of daily cases. It was observed that artificial neural networks could not adapt to these changes quickly. For the training of the network, it is thought that optimization algorithms with the ability to scan the entire search space should be preferred. Conclusions: In this study, it has been concluded that models that can predict the course of pandemic diseases can be made with artificial neural networks and thus, measures to prevent the spread of the disease can be taken in a timely manner.