An unconditionally stable nonstandard finite difference method to solve a mathematical model describing Visceral Leishmaniasis
Loading...
Date
2021
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
In this paper, a mathematical model of Visceral Leishmaniasis is considered. The model incorporates three populations, the human, the reservoir and the vector host populations. A detailed analysis of the model is presented. This analysis reveals that the model undergoes a backward bifurcation when the associated reproduction threshold is less than unity. For the case where the death rate due to VL is negligible, the disease-free equilibrium of the model is shown to be globally-asymptotically stable if the reproduction number is less than unity. Noticing that the governing model is a system of highly nonlinear differential equations, its analytical solution is hard to obtain. To this end, a special class of numerical methods, known as the nonstandard finite difference (NSFD) method is introduced. Then a rigorous theoretical analysis of the proposed numerical method is carried out. We showed that this method is unconditionally stable. The results obtained by NSFD are compared with other well-known standard numerical methods such as forward Euler method and the fourth-order Runge–Kutta method. Furthermore, the NSFD preserves the positivity of the solutions and is more efficient than the standard numerical methods.
Description
Keywords
Leishmaniasis, Mathematical modeling, Nonstandard finite difference method, Stability analysis, Death rates
Citation
Adamu, E.M. et al. (2021). An unconditionally stable nonstandard finite difference method to solve a mathematical model describing Visceral Leishmaniasis. Mathematics and Computers in Simulation ,187, 171-190