Abstract
This paper analyzes the properties of a continuous-time epidemic model used to describe infectious diseases such as COVID-19 and Tuberculosis (TB) and how controlled and tracked it using optimal control theory. The dynamic behavior of the epidemiological model is analyzed using the SIR (Susceptible-Infected-Recovery) model, where different values of parameters of the epidemic model will be simulated using MATLAB program to better understand and to extract useful information about possible situations. The behavior of the infectious disease COVID-19 and TB is investigated with real data in Libya and controlled using a Pontryagin Minimum Principle (PMP) which characterizes optimality around the optimal solution to minimizing the infected people and maximizing the recovery process. The simulation results indicate that the designed control strategy has a positive effect. In addition, the Graphical User Interface (GUI) was designed to know the behavior of other epidemics and how they can be controlled and thus by increasing or decreasing one of the parameters of that disease without the need to use mathematical operations to solve differential equations.