Optimal Control Synthesis of Epidemic Model

Abstract

The spread of a virus or the outbreak of an epidemic are natural examples of stochastic processes. Understanding the epidemic dynamics, and finding out efficient techniques to control it, is a challenging issue. This paper investigates the optimal use of intervention strategies to mitigate the spread of infectious diseases. Classical mathematical descriptions of such phenomenon include various branching processes such as the SIR (Susceptible-Infected-Recovered). One reason for mathematical modelling is to analyze and predict the extent of emerging diseases and develop proposed control measures. The quadratic regulator format was used to formulate the optimal control problem, and two different optimal control techniques were investigated: Single Network Adaptive Critic (SNAC), which is a direct application of reinforcement learning theory to the optimality necessary conditions, and Approximate Sequence Riccati Equation (ASRE), which is a global optimal feedback control technique for general nonlinear systems with nonquadratic performance criteria. According to the results obtained during simulations, we claim that the proposed model and control strategy can be considered a good candidate to study viral spreading in the world. Also, the result shows that the Single Network Adaptive Critic is more accurate than the Approximate Sequence Riccati Equation.