Analysis of the mathematical model of cutaneous Leishmaniasis disease

Abstract

Mathematical models are powerful tools to study various real-world problems from different perspectives. This branch has been given much more popularity over the last several decades. Various mathematical models corresponding to different diseases have been studied so far. Keeping these details in mind, the present manuscript is devoted to present a detailed mathematical analysis of the Cutaneous Leishmaniasis disease model. Some basic properties of the model are studied including positivity, the existence of equilibrium points, and reproductive number. The existence and uniqueness of the solution for the model under consideration are also investigated. Local and global stability analyses of equilibrium points are also studied. For the required results, we use the Lyapunov function method and the third additive compound matrix technique based on the Metzler procedure. Sensitivity analysis is also investigated by using some tools from the numerical-functional analysis. A numerical analysis of the proposed model is performed by using a nonstandard finite difference scheme. Moreover, for the justification of our results, we give some graphical presentation of the model for each class in the model. Also, we present some graphical presentations related to the sensitivity analysis along with the tables for its various indices.

Keywords

• Leishmaniasis Disease model
• Local and global stability
• Sensitivity Analysis
• Numerical analysis
• Non standard finite difference method