Modeling and analysis of visceral leishmaniasis dynamics using fractional‐order operators: A comparative study

Abstract

An in‐depth understanding of the mechanism concerning the parasitic disease called visceral leishmaniasis (VL) remains challenging. Thus, we modeled the dynamics of this illness using two fractional‐order operators, including Caputo–Fabrizio and Atangana–Baleanu. In the proposed dynamical model, the endemic and disease‐free equilibrium points were considered the symmetrical components. The fractional Euler method was applied to simulate the developed model, thus determining the equilibrium points' stability. The numerical simulation results were compared with the measured data to validate the model. The results obtained from the optimum fractional operator disclosed the minimum absolute and relative errors. The primary outcome of our study is the successful application of fractional‐order operators, specifically the Atangana–Baleanu operators with = 0.98, in modeling the dynamics of VL. Notably, the numerical simulation results, validated against real data from Sudan, demonstrated that the Atangana–Baleanu operators with = 0.98 yielded the best performance, with minimum absolute and relative errors. This underscores the precision of our fractional calculus‐based dynamical model in predicting VL dynamics compared to the classical framework, particularly for fractional‐order values of = 0.99 and = 0.98.