Application of Pontryagin's Minimum Principle in the Artificial Neural Network to Reduce the COVID-19 Pandemic Effects

In this study, we analyze the optimal intervention strategies that lead to reducing the effects of the COVID-19 pandemic by artificial neural networks (ANNs). Our aim is to investigate the effects of optimal control strategies, such as the implementation of government intervention, testing, and vaccination policies during outbreaks. We utilized a controlled SIDAREV model to study the progression of the COVID-19 pandemic. Using Pontryagin's minimum principle (PMP) for the SIDAREV model, we defined an unconstrained minimization problem. Applying the Hamiltonian conditions, we approximated the obtained ordinary differential equations (ODE) using ANNs. We utilized the multilayer perceptron (MLP) to obtain the approximate solution of the states and co-states functions. We observed the effects of optimal control strategies, and to show the efficiency of the proposed method, we compared it with the Runge-Kutta method through some examples. Using a mathematical model that simulates the behavior of the Covid-19 disease, we can examine the effects of controllers such as government interventions, tests and vaccinations with the neural network method. The results show that this method is useful in solving the problem of optimal control of infectious diseases.