Design a robust sliding mode controller based on the state and parameter estimation for the nonlinear epidemiological model of Covid-19.

In this research, the challenging problem of Covid-19 mitigation is looked at from an engineering point of view. At first, the behavior of coronavirus in the Iranian and Russian societies is expressed by a set of ordinary differential equations. In the proposed model, the control input signals are vaccination, social distance and facial masks, and medical treatment. The unknown parameters of the system are estimated by long short-term memory (LSTM) algorithm. In the LSTM algorithm, the problem of long-term dependency is prevented. The uncertainty and measurement noises are inherent characteristics of epidemiological models. For this reason, an extended Kalman filter (EKF) is developed to estimate the state variables of the proposed model. In continuation, a robust sliding mode controller is designed to control the spread of coronavirus under vaccination, social distance and facial masks, and medical treatment. The stability of the closed-loop system is guaranteed by the Lyapunov theorems. The official confirmed data provided by the Iranian and Russian ministries of health are employed to simulate the proposed algorithms. It is understood from simulation results that global vaccination has the potential to create herd immunity in long term. Under the proposed controller, daily Covid-19 infections and deaths become less than 500 and 10 people, respectively.