Model of transmission of three types Leprosy Disease with treatment

Leprosy disease is caused by infection of Mycobacterium leprae that affects the skin and nerve. The treatment duration for leprosy takes 6 to 24 months with multi-drug therapy. In this article, a 6-d mathematical model for transmission of three types leprosy disease with treatment was constructed. Analysis and numerical simulation were done to explore the existence and stability of equilibrium points and basic reproduction number R0. The local stability of endemic equilibrium point was done by numerical simulation. Numerical simulation also confirmed that the disease-free equilibrium is locally asymptotically stable when R0 < 1 and the endemic equilibrium point locally asymptotically stable when R0 > 1. Numerical simulation was also done to show the sensitivity of R0 with respect to some contact parameters. The result showed that the change of contact rate between susceptible people and lepromatous type infected hosts has more effect to change the value of R0. The reduction of contact rate between susceptible people and lepromatous type infected hosts is more effective to control prevention leprosy disease compared with tuberculoid and borderline types.