Exact solutions to fractional pharmacokinetic models using multivariate Mittag-Leffler functions

Morales‐Delgado, V. F.; Taneco-Hernández, M.A.; Vargas‐De‐León, Cruz; Gómez‐Aguilar, J.F.

doi:10.1016/j.chaos.2023.113164

Cited by 12 publications

(4 citation statements)

References 40 publications

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“…In this direction, the recent results of [25] may be useful. Moreover, we plan to investigate PK/PD fractional-order models, which is a subject under strong current research [26]. This is under investigation and will be addressed elsewhere.…”

Section: Discussionmentioning

confidence: 99%

An Analytic Method to Determine the Optimal Time for the Induction Phase of Anesthesia

Zaitri,

Silva,

Torres

2023

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We obtain an analytical solution for the time-optimal control problem in the induction phase of anesthesia. Our solution is shown to align numerically with the results obtained from the conventional shooting method. The induction phase of anesthesia relies on a pharmacokinetic/pharmacodynamic (PK/PD) model proposed by Bailey and Haddad in 2005 to regulate the infusion of propofol. In order to evaluate our approach and compare it with existing results in the literature, we examine a minimum-time problem for anesthetizing a patient. By applying the Pontryagin minimum principle, we introduce the shooting method as a means to solve the problem at hand. Additionally, we conducted numerical simulations using the MATLAB computing environment. We solve the time-optimal control problem using our newly proposed analytical method and discover that the optimal continuous infusion rate of the anesthetic and the minimum required time for transition from the awake state to an anesthetized state exhibit similarity between the two methods. However, the advantage of our new analytic method lies in its independence from unknown initial conditions for the adjoint variables.

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Section: Discussionmentioning

confidence: 99%

An Analytic Method to Determine the Optimal Time for the Induction Phase of Anesthesia

Zaitri,

Silva,

Torres

2023

Axioms

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“…The proposed model shows a limitation in data fit profiles, without transgressing the fundamental principles of mass balance and physiological states. The mathematical study of the amount of drug administered as a continuous intravenous infusion or oral dose for fractional-order mammillary type models is investigated in [30].…”

Section: Introductionmentioning

confidence: 99%

Pharmacokinetic/Pharmacodynamic anesthesia model incorporating psi-Caputo fractional derivatives

Zaitri,

Zitane,

Torres

2023

Computers in Biology and Medicine

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“…The Atangana-Baleanu-Caputo (ABC) fractional derivative provides an accurate description of the memory [43]. The important applications of the ABC operator can be found in [44], [45], [46], [47], [48], [49], [50], [51], [52], [53], [54], [55], [56], [57], and [58]. Recently, it has been observed that fractional differential equations can be employed to modeling phenomena of worldwide more accurately.…”

Section: Introductionmentioning

confidence: 99%

Generalized Defensive Modeling of Malware Propagation in WSNs Using Atangana–Baleanu– Caputo (ABC) Fractional Derivative

Srivastava¹,

Srivastava²,

Mishra³

et al. 2023

IEEE Access

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The malware spreading in Wireless Sensor Network (WSN) has lately attracted the attention of many researchers as a hot problem in nonlinear systems. WSN is a collection of sensor nodes that communicate with each other wirelessly. These nodes are linked in a decentralised and distributed structure, allowing for efficient data collection and communication. Due to their decentralised architecture and limited resources, WSN is vulnerable to security risks, including malware attacks. Malware can attack sensor nodes, causing them to malfunction and consume more energy. These attacks can spread from one infected node to others in the network, making it essential to protect WSN against malware attacks. In this paper, we focus on the analysis of a novel fractional epidemiology model, specifically the fractional order SEIVR epidemic model in the sense of Caputo's fractional derivative of order 0< α≤1 with the goal of examining the efficacy of vaccination strategies and the heterogeneity of a scale-free network on epidemic spreading. First, using the next-generation technique and obtain the basic reproduction number of the proposed epidemic model, which is essential for determining both the locally asymptotically stable equilibrium point of the wormfree system and the unique existence of the endemic equilibrium point. To numerically solve the model, the Adam-Bashforth-Moulton predictor-corrector (ABM) method is applied. The fractional calculus enables us to deal directly with the ''memory effect'' of numerous phenomena, taking into account the system's dependence on previous stages. This method provides the results of a complex system. Additionally, research demonstrates that vaccine treatments are quite effective at preventing the spread of malware. The outcome of the study reveals that the applied ABM predictor-corrector method is computationally strong and effective to analyse fractional order dynamical systems in the SEIVR epidemic model for malware propagation in WSN. The results show that the order of the fractional derivative has a significant effect on the dynamic process. Also, from the result, it is obvious that the memory effect is zero for α = 1. When the fractional order α is decreased from 1, the memory effect appears, and its dynamics vary according to the time. This memory effect points out the difference between derivatives of fractional and integer orders. The theorems and their proofs are presented to validate the validity of the proposed model. To validate the proposed model, extensive theoretical study and computational analysis have also been applied.The associate editor coordinating the review of this manuscript and approving it for publication was Stefano Scanzio .

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Exact solutions to fractional pharmacokinetic models using multivariate Mittag-Leffler functions

Cited by 12 publications

References 40 publications

An Analytic Method to Determine the Optimal Time for the Induction Phase of Anesthesia

An Analytic Method to Determine the Optimal Time for the Induction Phase of Anesthesia

Pharmacokinetic/Pharmacodynamic anesthesia model incorporating psi-Caputo fractional derivatives

Generalized Defensive Modeling of Malware Propagation in WSNs Using Atangana–Baleanu– Caputo (ABC) Fractional Derivative

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