Nonstandard finite difference approach for solving 3‐compartment pharmacokinetic models

Egbelowo, Oluwaseun Francis

doi:10.1002/cnm.3114

Cited by 14 publications

(13 citation statements)

References 10 publications

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“…Nowadays, NSFD schemes have been widely used as a powerful and efficient class of numerical methods for solving differential equations arising in real-world situations. We refer the readers to [32][33][34][35][36][37][38][39] and [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] for good reviews and some recent notable works related to NSFD schemes, respectively. Recently, we have successfully developed the Mickens' methodology to construct NSFD schemes for differential equation models arising in real-world applications [55][56][57][58][59][60].…”

Section: Introductionmentioning

confidence: 99%

A simple method for studying asymptotic stability of discrete dynamical systems and its applications

Hoang

Ngo²,

Truong

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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In this work, we introduce a simple method for investigating the asymptotic stability of discrete dynamical systems, which can be considered as an extension of the classical Lyapunov's indirect method. This method is constructed based on the classical Lyapunov's indirect method and the idea proposed by Ghaffari and Lasemi in a recent work. The new method can be applicable even when equilibia of dynamical systems are non-hyperbolic. Hence, in many cases, the classical Lyapunov's indirect method fails but the new one can be used simply. In addition, by combining the new stability method with the Mickens' methodology, we formulate some nonstandard finite difference (NSFD) methods which are able to preserve the asymptotic stability of some classes of differential equation models even when they have non-hyperbolic equilibrium points. As an important consequence, some well-known results on stability-preserving NSFD schemes for autonomous dynamical systems are improved and extended. Finally, a set of numerical examples are performed to illustrate and support the theoretical findings.

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Section: Introductionmentioning

confidence: 99%

A simple method for studying asymptotic stability of discrete dynamical systems and its applications

Hoang

Ngo²,

Truong

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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“…Therefore, they are efficient and appropriate to simulate behaviour of dynamical differential equation models over long time periods. Nowadays, NSFD schemes have become an efficient approach for numerically solving real-world problems (see, for example, [1,2,4,5,10,13,14,15,31,32,47,48,57,58]). Recently, we have developed the Mickens' methodology to construct NSFD schemes for mathematical models of phenomena and processes coming from sciences and technology like biology, ecology, or other natural sciences [16,17,18,19,20,21,25,26,27,28,29].…”

Section: Introductionmentioning

confidence: 99%

A dynamically consistent nonstandard finite difference scheme for a generalized SEIR epidemic model

Hoang

2023

Preprint

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Although Coronavirus disease 2019 (COVID-19) pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been controlled and prevented, mathematical modeling and analysis of transmission dynamics of COVID-19 still plays an essential role not only in the post COVID-19 era but also in the study of infectious diseases. This is an important foundation to propose effective strategies and measures for controlling diseases and projecting public health. This work is devoted to proposing and analyzing a new mathematical study for transmission dynamics of COVID-19. We first introduce a generalized SEIR epidemic model that use general nonlinear incidence rates to describe the “psychological” effect. After that, a rigorous mathematical analysis for the proposed COVID-19 model is performed. We establish the positivity and boundedness, calculate the basic reproduction number, determine possible (disease-free and endemic-disease) equilibrium points and investigate their asymptotic stability properties of the SEIR model. The obtained results improve and extend an SEIR model constructed in a recent work. For the purpose of numerical simulation, the Mickens’ methodology is applied to construct a dynamically consistent nonstandard finite difference (NSFD) model for the proposed SEIR epidemic model. The constructed NSFD scheme has the ability to provide reliable approximations that not only preserve the dynamical properties of the SEIR model for all the values of the step size but also are easy to be implemented. Finally, a set of illustrative numerical experiments is conducted to support the theoretical findings and to confirm advantages of the NSFD scheme over some well-known standard ones.

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“…In this study we considered accurate solutions of two types of models (see Khanday et al, 5 Egbelowo, 8 Cascone et al, 9 and Bailey and Shafer 10 ), which consist of II and III compartments for drug absorption and circulation through GIT and blood stream. This is to help estimate the drug concentration at different parts of the body within the blood stream.…”

Section: Introductionmentioning

confidence: 99%

“…According to some experiments carried out experimentally, the dosage of medicine varies from one individual patient to another depending upon the condition and severity of the disease. 6,7 In this study we considered accurate solutions of two types of models (see Khanday et al, 5 Egbelowo, 8 Cascone et al, 9 and Bailey and Shafer 10 ), which consist of II and III compartments for drug absorption and circulation through GIT and blood stream. This is to help estimate the drug concentration at different parts of the body within the blood stream.…”

Section: Introductionmentioning

confidence: 99%

Accurate numerical integration of highly stiff pharmacokinetics models using continuous block implicit hybrid one-step collocation methods

Yakubu

Abdulhameed

Adamu

et al. 2023

Journal of Algorithms & Computational Technology

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The differential equations of pharmacokinetic models, obtained from the formulation based on the Fick's perfusion principle and law of conservation of mass action, deals with absorption, distribution, and elimination of drugs by the body systems. In the formulation, the ordinary differential equations obtained may result into highly stiff systems whereby suitable implicit methods have to be employed to solve accurately drug concentration in the body systems, owing to the complex nature of the exact solutions, if they exist. Further, because of the large and increasing interest in the problems of drug kinetics, it is necessary to apply considerably accurate implicit numerical methods in evaluating and in applying them to specific cases. These solutions are to help determine the distribution of drug concentration in different compartments (parts) of the human body network systems as a fundamental step to help in understanding and improving treatments. This is necessary since drug concentration in each compartment is different from one another because of the differences in drug affinity to tissues. From the study, the solution curves obtained show that drug level in the gastrointestinal tract decreases with the passage of time, while drug concentration in the blood increases from zero and reaches its maximum level and then decreases steadily again. We further, compared the model curves with some experimental data plots published in scientific papers. The results obtained from the study can be used extensively for various drug diffusion problems arising in pharmaceutical studies. The presented results widen the applicability of the continuous block implicit hybrid one-step collocation methods to diffusion process which have good number of applications in the drug control, drug dosage and other related problems in pharmaceutical and biomedical industries.

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Nonstandard finite difference approach for solving 3‐compartment pharmacokinetic models

Cited by 14 publications

References 10 publications

A simple method for studying asymptotic stability of discrete dynamical systems and its applications

A simple method for studying asymptotic stability of discrete dynamical systems and its applications

A dynamically consistent nonstandard finite difference scheme for a generalized SEIR epidemic model

Accurate numerical integration of highly stiff pharmacokinetics models using continuous block implicit hybrid one-step collocation methods

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