An unconditionally stable nonstandard finite difference method to solve a mathematical model describing Visceral Leishmaniasis
| dc.contributor.author | Adamu, E.M | |
| dc.contributor.author | Patidar, K.C | |
| dc.contributor.author | Ramanantoanina, A | |
| dc.date.accessioned | 2021-04-15T07:34:42Z | |
| dc.date.available | 2021-04-15T07:34:42Z | |
| dc.date.issued | 2021 | |
| dc.description.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. | en_US |
| dc.identifier.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 | en_US |
| dc.identifier.issn | 0378-4754 | |
| dc.identifier.uri | 10.1016/j.matcom.2021.02.007 | |
| dc.identifier.uri | http://hdl.handle.net/10566/6033 | |
| dc.language.iso | en | en_US |
| dc.publisher | Elsevier | en_US |
| dc.subject | Leishmaniasis | en_US |
| dc.subject | Mathematical modeling | en_US |
| dc.subject | Nonstandard finite difference method | en_US |
| dc.subject | Stability analysis | en_US |
| dc.subject | Death rates | en_US |
| dc.title | An unconditionally stable nonstandard finite difference method to solve a mathematical model describing Visceral Leishmaniasis | en_US |
| dc.type | Article | en_US |