Computational dynamics of a fractional order substance addictions transfer model with Atangana‐Baleanu‐Caputo derivative

Abstract

In this paper, the ABC fractional derivative is used to provide a mathematical model for the dynamic systems of substance addiction. The basic reproduction number is investigated, as well as the equilibrium points' stability. Using fixed point theory and nonlinear analytic techniques, we verify the theoretical results of solution existence and uniqueness for the proposed model. A numerical technique for getting the approximate solution of the suggested model is established by using the Adams type predictor‐corrector rule for the ABC‐fractional integral operator. There are several numerical graphs that correspond to different fractional orders. Furthermore, we present a numerical simulation for the transmission of substance addiction in two scenarios with fundamental reproduction numbers greater than and fewer than one.

الحلول شبه التحليلية لمعادلات فيشر الكسرية للزمن عبر الطريقة التكرارية الجديدة

“…The study also examines the interaction between prey and predator populations, focusing on the additive Allee effect and intraspecific competition. The study highlights the importance of considering precautionary measures in controlling disease spread, with the rate of precautionary measures playing a crucial role in reducing the chance of infection by the Chickenpox virus [23][24][25] .…”

“…The study of investigates solutions for nonlinear generalized proportional, fractional functional integro-differential Langevin equations using fixed point theorems and Ulam-Hyers stability. It creates a mathematical model to analyse Wolbachia dispersal among Aedes aegypti mosquitoes, analysing symmetrical characteristics [20][21][22] . The model is physically meaningful and assessed for equilibrium points in the presence and absence of disease.…”

A generalized fractional hepatitis B virus infection modelwith both cell-to-cell and virus-to-cell transmissions

“…Fractional order equations provide a more realistic representation of the dynamics of disease because they take into consideration the memory effect, which means that the current and the past behavior of the state determine the future state of the fractional operator of a given function [4]. The dynamic of the transmission of several infectious diseases is described by many works using this derivation [5][6][7][8][9][10][11][12][13][14][15][16]. Recently Yang et al [17], studied a fractional epidemic model of HBV adaptive immunity.…”

Understanding COVID-19 propagation: a comprehensive mathematical model with Caputo fractional derivatives for Thailand

“…In 2023, the study examined the effectiveness of precautionary measures in managing chickenpox in Phuket by utilizing mathematical modeling and conducting bifurcation analysis to evaluate potential outcomes [1], and also in Jose et al [2] the authors have developed and analyzed a deterministic mathematical model to investigate the transmission dynamics of co-infection involving Dengue Fever (DF) and Zika virus (ZIKV), also Van den Driessche and Watmough [3] presents a twostrain epidemic mathematical model that incorporates vaccination strategies, as discussed in the journal Computer Methods in Biomechanics and Biomedical Engineering and also in Joseph et al [4] discusses a fractional-order density-dependent mathematical model aimed at identifying the superior strain of Wolbachia, available as an open access article with options for ordering article reprints and citations. Similarly in 2022, a stuy focused on the computational dynamics of a fractional order substance addictions transfer model incorporating the Atangana-Baleanu-Caputo derivative was conducted [5]. And Thomas et al [6] delves into modeling and analyzing SEIRS epidemic models, specifically focusing on the 2019-nCoV outbreak in India, utilizing the homotopy perturbation method.…”