Optimal control strategies based on extended Kalman filter in mathematical models of COVID-19

Abstract

The Omicron variant of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus is an extremely contagious variant that has garnered global attention due to its potential for rapid spread and its impact on the effectiveness of vaccines and non-pharmacological measures. In this paper, we investigate mathematical models involving vaccinated individuals and control functions to analyze how the spread of coronavirus disease 2019 (COVID-19) infection evolves over time. In the process of constructing a mathematical model for COVID-19, there are many parameters whose values are not yet known with certainty. Therefore, the extended Kalman filter method is used as a tool to estimate these parameters in an effort to better understand the dynamics of the spread and evolution of this disease. This method helps align the mathematical model with existing empirical data, allowing us to make more accurate predictions about the course of the COVID-19 pandemic and plan more precise actions to address the situation. Furthermore, an optimal control design is applied to reduce the number of infected individuals by implementing seven strategies involving a combination of health education, vaccination, and isolation controls. The simulation results we conducted indicate that the use of optimal control strategies can lead to a significant decrease in the number of individuals infected with COVID-19.