scholarly journals Effects of Drugs Reabsorption Time Delays for a Pharmacokinetics Model in Humans

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Adamu Shitu Hassan ◽  
Justin M. W. Munganga
Keyword(s):  
Sensitivity Analysis ◽  
Time Delays ◽  
Equilibrium Points ◽  
Compartment Model ◽  
Central Compartment ◽  
Asymptotically Stable ◽  
Delay Model ◽  
Time Profiles ◽  
Model Dynamics ◽  
Oral Doses

A three-compartmental delay model is formulated to describe the pharmacokinetics of drugs subjected to both intravenous and oral doses with reabsorptions by the central compartment. Model dynamics are analyzed rigorously, and two equilibrium points are obtained to be locally asymptotically stable under certain conditions. Time delays used as lags in reabsorption of drugs by central compartment from other two compartments caused rebounds or peaks and fluctuations in the time profiles for amounts of drug in all the compartments. Sensitivity analysis revealed that elimination rates decrease the amounts in all compartments. Furthermore, reabsorption rates cause superimposition at the initial phases of the drug amount profiles; subsequently, the quantities decrease in compartment one and increase in compartments two and three, respectively.

scholarly journals Global Stability of Malaria Transmission Dynamics Model with Logistic Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Abadi Abay Gebremeskel
Keyword(s):  
Sensitivity Analysis ◽  
Global Stability ◽  
Malaria Transmission ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Dynamics Model ◽  
Globally Asymptotically Stable ◽  
The Impact

Mathematical models become an important and popular tools to understand the dynamics of the disease and give an insight to reduce the impact of malaria burden within the community. Thus, this paper aims to apply a mathematical model to study global stability of malaria transmission dynamics model with logistic growth. Analysis of the model applies scaling and sensitivity analysis and sensitivity analysis of the model applied to understand the important parameters in transmission and prevalence of malaria disease. We derive the equilibrium points of the model and investigated their stabilities. The results of our analysis have shown that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if R0>1, then the unique endemic equilibrium point is globally asymptotically stable and the disease persists within the population. Furthermore, numerical simulations in the application of the model showed the abrupt and periodic variations.

scholarly journals A mathematical model for malaria transmission relating global warming and local socioeconomic conditions

2001 ◽  
Vol 35 (3) ◽  
pp. 224-231 ◽  
Author(s):  
Hyun M Yang
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Global Warming ◽  
Malaria Transmission ◽  
Equilibrium Points ◽  
Compartment Model ◽  
Malaria Risk ◽  
Model Parameters ◽  
Socioeconomic Conditions ◽  
The Mathematical Model

OBJECTIVE: Sensitivity analysis was applied to a mathematical model describing malaria transmission relating global warming and local socioeconomic conditions. METHODS: A previous compartment model was proposed to describe the overall transmission of malaria. This model was built up on several parameters and the prevalence of malaria in a community was characterized by the values assigned to them. To assess the control efforts, the model parameters can vary on broad intervals. RESULTS: By performing the sensitivity analysis on equilibrium points, which represent the level of malaria infection in a community, the different possible scenarios are obtained when the parameters are changed. CONCLUSIONS: Depending on malaria risk, the efforts to control its transmission can be guided by a subset of parameters used in the mathematical model.

scholarly journals P72 Maturation of sildenafil clearance in prematurely born infants with BPD associated pulmonary hypertension

2019 ◽  
Vol 104 (6) ◽  
pp. e47.1-e47
Author(s):  
H Nikrawesh ◽  
AGJ Engbers ◽  
S Völler ◽  
SHP Simons ◽  
BCP Koch ◽  
...  
Keyword(s):  
Pulmonary Hypertension ◽  
Compartment Model ◽  
Volume Of Distribution ◽  
Limited Information ◽  
Mixed Effect ◽  
Time Profiles ◽  
Nonlinear Mixed Effect ◽  
Postmenstrual Age ◽  
Oral Doses ◽  
Prematurely Born Infants

BackgroundSildenafil is used as an off-label treatment for bronchopulmonary dysplasia (BPD) associated pulmonary hypertension in prematurely born infants. As there is only limited information on the pharmacokinetics (PK) of sildenafil in this population, the aim of this study is to investigate the PK of sildenafil in prematurely born infants with BPD associated pulmonary hypertension.MethodIn this multicentre study, a population PK model for sildenafil in prematurely born infants was developed based on samples obtained using opportunistic sampling during clinical use of sildenafil. Data of seven subjects (42 plasma samples) were analysed by nonlinear mixed-effect modelling (NONMEM®7.3). Median (range) gestational age (GA) was 26.1 (24.1–27.6) weeks, current bodyweight 1960 (632–3157) grams, birthweight 635 (465–1125) grams and postnatal age (PNA) at start of therapy 64.9 (10.9–89) days. The median (range) treatment duration was 4.9 (1.6–13.1) weeks, with six subjects receiving oral doses of median 2.6 mg/kg/day (1.5–5.3) in three doses and one subject receiving oral and intravenous doses of 6.7 mg/kg/day in two doses.ResultsThe plasma concentration time profiles of sildenafil were best described by a one compartment model. Clearance (CL) and volume of distribution (Vd) for a child with a PNA of 64.9 days and bodyweight of 1.96 kg was 4.42 L/h ((RSE) 11%) and 29.5 L (32%), respectively. PNA was found to significantly influence CL, resulting in an increase of 10.7% in a week, and 43% in a month for a 65-day old infant. No other covariates (i.e. bodyweight, birthweight, GA, postmenstrual age and sex) were identified for CL or Vd.ConclusionIn this PK study, we characterised the pharmacokinetics of sildenafil in prematurely born infants and found that clearance increases with PNA. Due to the limited sample size in this study, further research in a larger population is needed to extend these findings.Disclosure(s)Nothing to disclose

Dynamics of a delayed competitive system affected by toxic substances with imprecise biological parameters

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5271-5293
Author(s):  
A.K. Pal ◽  
P. Dolai ◽  
G.P. Samanta
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Toxic Substances ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Competitive System ◽  
Interval Numbers ◽  
Cycle Oscillation

In this paper we have studied the dynamical behaviours of a delayed two-species competitive system affected by toxicant with imprecise biological parameters. We have proposed a method to handle these imprecise parameters by using parametric form of interval numbers. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate our analytical findings.

scholarly journals Global Stability Analysis of a Bioreactor Model for Phenol and Cresol Mixture Degradation

Processes ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 124
Author(s):  
Neli Dimitrova ◽  
Plamena Zlateva
Keyword(s):  
Specific Growth ◽  
Equilibrium Points ◽  
Nonlinear Ordinary Differential Equations ◽  
The Novel ◽  
Model Design ◽  
Stirred Bioreactor ◽  
Global Stability Analysis ◽  
Local Asymptotic Stability ◽  
Model Dynamics ◽  
Stability And Bifurcations

We propose a mathematical model for phenol and p-cresol mixture degradation in a continuously stirred bioreactor. The model is described by three nonlinear ordinary differential equations. The novel idea in the model design is the biomass specific growth rate, known as sum kinetics with interaction parameters (SKIP) and involving inhibition effects. We determine the equilibrium points of the model and study their local asymptotic stability and bifurcations with respect to a practically important parameter. Existence and uniqueness of positive solutions are proved. Global stabilizability of the model dynamics towards equilibrium points is established. The dynamic behavior of the solutions is demonstrated on some numerical examples.

scholarly journals Threshold dynamics and threshold analysis of HIV infection model with treatment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Zhimin Chen ◽  
Xiuxiang Liu ◽  
Liling Zeng
Keyword(s):  
Hiv Infection ◽  
Time Delays ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Threshold Dynamics ◽  
Positive Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Immunodeficiency Virus ◽  
Hiv Infection Model

Abstract In this paper, a human immunodeficiency virus (HIV) infection model that includes a protease inhibitor (PI), two intracellular delays, and a general incidence function is derived from biologically natural assumptions. The global dynamical behavior of the model in terms of the basic reproduction number $\mathcal{R}_{0}$ R 0 is investigated by the methods of Lyapunov functional and limiting system. The infection-free equilibrium is globally asymptotically stable if $\mathcal{R}_{0}\leq 1$ R 0 ≤ 1 . If $\mathcal{R}_{0}>1$ R 0 > 1 , then the positive equilibrium is globally asymptotically stable. Finally, numerical simulations are performed to illustrate the main results and to analyze thre effects of time delays and the efficacy of the PI on $\mathcal{R}_{0}$ R 0 .

Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation

2021 ◽  
Author(s):  
Adwait Verulkar ◽  
Corina Sandu ◽  
Daniel Dopico ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Multibody Systems ◽  
Friction Model ◽  
Design Parameters ◽  
Adjoint Sensitivity ◽  
Joint Friction ◽  
Multibody Dynamic ◽  
Model Dynamics ◽  
Direct Sensitivity

Abstract Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.

Chaos in the Periodically Parametrically Excited Lorenz System

2021 ◽  
Vol 31 (08) ◽  
pp. 2130024
Author(s):  
Weisheng Huang ◽  
Xiao-Song Yang
Keyword(s):  
Chaotic Dynamics ◽  
Lorenz System ◽  
Stable Equilibrium ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Parametrically Excited ◽  
The Lorenz System

We demonstrate in this paper a new chaotic behavior in the Lorenz system with periodically excited parameters. We focus on the parameters with which the Lorenz system has only two asymptotically stable equilibrium points, a saddle and no chaotic dynamics. A new mechanism of generating chaos in the periodically excited Lorenz system is demonstrated by showing that some trajectories can visit different attractor basins due to the periodic variations of the attractor basins of the time-varying stable equilibrium points when a parameter of the Lorenz system is varying periodically.

Super-Resolution Time-Delays Estimation in HF Channel Sounding Based on Chirp Sequence

2011 ◽  
Vol 204-210 ◽  
pp. 2133-2139
Author(s):  
Long Fei Fu ◽  
Gang Xin ◽  
Shui Lian Zhang
Keyword(s):  
Time Delay ◽  
Time Delays ◽  
Measurement Data ◽  
Super Resolution ◽  
Wide Band ◽  
Estimation Problem ◽  
Delay Model ◽  
Music Algorithm ◽  
Problem Of Time ◽  
Hf Channel

According to the characteristics of HF channel and chirp signal, an innovative multipath time-delay model of wide-band HF channel was proposed, by which the estimation problem of time-delay was converted into an estimation problem of spectrum.Then the MUSIC algorithm with super-resolution ability was applied to the problem above. The feasibility of estimating multipath time-delays based on single measurement data was deeply discussed. Meanwhile, the performance of applying MUSIC and root MUSIC algorithm to the model proposed in the paper was presented. The simulation results suggested that the method proposed in the paper owned super-resolution ability and robust in estimation of multipath time-delay.

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