A mathematical model of tuberculosis transmission in Thailand with vaccination and anti-drug treatment

Abstract

Tuberculosis is a contagious disease caused by Mycobacterium tuberculosis which can spread from person to person through the air by breathing, coughing and sneezing or staying with the patients for a long time. In Thailand, there is a high tuberculosis problem since each year the number of patients and resistant patients increased. In this project, we construct a mathematical model of Tuberculosis in Thailand with vaccination and anti-drug treatment. The model consists of susceptible, vaccination, exposed, infected, resistant and recovered. Then we find equilibrium points, investigate the stability of equilibrium points, a basic reproduction number by using next-generation method and sensitivity analysis on the basic reproduction number. Next, we provide numerical solutions by using Fourth order Runge-Kutta and then comparing numerical solutions with information of patients from 2014 to 2017 found that the error was 9.6024 percent. Furthermore, we improve the numerical solution by simple linear regression and polynomial regression. We found that the error decreased by about 2 percent.