A neural network approach for optimal control of SEIQRS epidemic models

In this study, we present a neural network-based approach to optimal control problems in the Susceptible-Exposed-Infectious-Quarantined-Recovered $(SEIQRS)$ epidemic model. In order to benefit from the capabilities of deep learning techniques. Our method involves encoding control functions in neural networks, enabling us to effectively address the complex challenges of epidemiological control. To address this method, we show first the existence of the solution for the optimal control model in the general form control case. Then, we use a neural network as an approximation method for the controls and rely on the adjoint state problem and the gradient descent method to update the value of the controls by updating the neural network parameter that is considered as an approximation. The proposed approach offers new perspectives for epidemic forecasting. The results obtained using the neural network approach demonstrate its effectiveness compared to direct collection for several types of models.