Application of Lyapunov Control for Analysis Spread of COVID-19 in Indonesia

COVID-19 (coronavirus disease 2019) is a respiratory tract infection transmitted from human to human, so the factor of human mobility plays an essential role in the spread of this disease. Moreover, with easy access to mobility between regions, the mobility of the population is increasing. It makes COVID-19 spread rapidly worldwide and results in a pandemic. This study examines the SEIR (Susceptible, Exposed, Infected, Removed) mathematical model of the spread of COVID-19 with the mobility aspect. The aspect of mobility reviewed is the displacement of each compartment S, E, I, and R between two cities. In actual conditions, the dynamics of the model can be disturbed by internal and external factors, resulting in differences from actual conditions. Therefore, we formulate a mathematical model of COVID-19 with the disturbance aspect. Then, the optimal control design based on the Lyapunov quadratic function will be formulated by forming the reference model and applying two control variables (vaccination and treatment) to minimize the number of exposed and infected individuals and stabilize the system. The reference model is in the form of a linear system with certain parameter values so that the system meets disease-free conditions. The parameter values in the controller design are estimated using a genetic algorithm to obtain a controller that can achieve control objectives and stabilize the system. Based on numerical simulation results using cumulative data on positive cases of COVID-19 in DKI Jakarta and West Java, Indonesia, the simultaneous application of vaccination control and treatment strategies was able to reduce the population of infected individuals in DKI Jakarta by 81.47% and in West Java by 73.98%.