𝒮‐asymptotically 𝓌‐periodic mild solutions for noninstantaneous impulsive integro‐differential equations with state‐dependent delay

Wang, Yinuo; Li, Chuandong; Deng, Hao; Wu, Hongjuan

doi:10.1002/mma.9177

Cited by 1 publication

(1 citation statement)

References 40 publications

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“…Intensive studies over the years revealed that mathematical modeling and simulation can play a significant role in understanding the reasons for diverse infectious diseases, thereby predicting the possible cure. It is needless to say that mathematical modeling of VL has a rich history wherein numerous reports exist on the classical, fractional, statistical, machine learning models, and so forth [1][2][3][4][5][6][7][8][9]. In addition, it was acknowledged that the fractional calculus can offer deep insights into the dynamics of VL, leading to more accurate model and effective treatment strategies.…”

Section: Introductionmentioning

confidence: 99%

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

Abdulkream Alharbi,

A. Abdoon,

Saadeh

et al. 2024

Math Methods in App Sciences

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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.

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