Global stability and optimal control of melioidosis transmission model with hygiene care and treatment

Abstract

Melioidosis is a bacterial disease and is mostly found in the tropical country especially Southeast Asia, Northern Australia and northeast Thailand. With an increase in number of infected patients and a belief that there is a large number of infections that is underreported, a better understanding and strategy approach in order to reduce the transmission is therefore required. In this study a compartmental model of melioidosis transmission involving hygiene care and treatment is presented. The model is analyzed theoretically and numerically. The basic reproduction number and its sensitivity indices are calculated. Further, by using Pontryagin???s Minimum Principle (PMP), the optimal control problem is constructed with two controls. Our results demonstrate that a combination of both hygiene care and treatment controls could largely help reducing the number of exposed and infected individuals and the concentration of bacteria. Therefore, both mentioned controls should be encouraged to reduce overall melioidosis transmission.??