Dynamics of Visceral Leishmania Epidemic Model with Non-Singular Kernel

In this paper, we have taken into consideration the most dangerous form of leishmaniasis known as visceral leishmaniasis, which has the highest fatality rate and is also famous with the name of kala-azar. The analysis is carried out using Atangana–Baleanu–Caputo (ABC) operator with a convex incidence rate. Using fixed point theorems the existence and uniqueness for the solutions of the fractional leishmania epidemic model have been established. All the basic properties of the given model are studied along with stability analysis. Newton polynomial and Adams–Bashforth methods are taken into account to find the numerical solution.