An unconditionally stable nonstandard finite difference method to solve a mathematical model describing Visceral Leishmaniasis

In this paper, a mathematical model of Visceral Leishmaniasis is considered. The incorporates three populations, the human, reservoir and vector host populations. A detailed analysis presented. This reveals that undergoes backward bifurcation when associated reproduction threshold less than unity. For case where death rate due to VL negligible, disease-free equilibrium shown be globally-asymptotically stable if number Noticing governing system highly nonlinear differential equations, its analytical solution hard obtain. To end, special class numerical methods, known as nonstandard finite difference (NSFD) method introduced. Then rigorous theoretical proposed carried out. We showed unconditionally stable. results obtained by NSFD are compared with other well-known standard methods such forward Euler fourth-order Runge–Kutta method. Furthermore, preserves positivity solutions more efficient methods. • analyze describing Leishmaniasis. very complex non-linear equations. design robust solve model. Proposed Method presented in paper competitive some classical