scholarly journals OL-052 A mathematical model with time-delay immune response for adefovir treatment

2009 ◽  
Vol 13 ◽  
pp. S46
Author(s):  
Shaopeng Chen ◽  
Yongmei Su ◽  
Lequan Min
Keyword(s):  
Mathematical Model ◽  
Immune Response ◽  
Time Delay

scholarly journals Dynamics Analysis of a Mathematical Model for New Product Innovation Diffusion

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Chunru Li ◽  
Zujun Ma
Keyword(s):  
Mathematical Model ◽  
Time Delay ◽  
Media Coverage ◽  
New Product ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Significant Difference ◽  
Form Theory ◽  
The Difference ◽  
The Stability

In this paper, a mathematical model with time-delay-related parameters and media coverage to describe the diffusion process of new products is proposed, in which the time-delay-related parameters denote the stage in which potential customers decide whether to adopt a new product. Then, the stability and the Hopf bifurcation of the proposed model are analyzed in detail. The center manifold theorem and the normal form theory are used to investigate the stability of the bifurcating periodic solution. Moreover, a numerical simulation is conducted to investigate the difference between the model with delay-dependent parameters and that with delay-independent parameters. The results show that there is significant difference between the two models.

scholarly journals Formulated Mathematical Model for Delayed Particle Flow in Cascaded Sub-Surface Water Reservoirs with Validation on River Flow

2018 ◽  
Author(s):  
Ombaki Richard ◽  
Kerongo Joash ◽  
Okwoyo M. James
Keyword(s):  
Mathematical Model ◽  
Time Delay ◽  
Surface Water ◽  
Discrete Time ◽  
River Flow ◽  
Water Reservoir ◽  
Point Sources ◽  
Water Reservoirs ◽  
Discrete Time Delay ◽  
Mixing Problem

Pollution of sub-surface water reservoirs mainly rivers and streams through contaminated water point sources (CWPS) was studied. The objective was to formulate a discrete time delay mathematical model which describes the dynamics of reservoir pollution using mixing-problem processes that involve single species contaminants such as nitrates, phosphorous and detergents. The concentration  of pollutants was expressed as a function of the inflow and outflow rates using the principle for the conservation of mass. Systems of ODEs generated from principles of mixing problems were refined into a system of DDEs so that the concentration of pollutant leaving the reservoir at time would be determined at some earlier instant, for the delay. The formulated model is a mathematical discrete time delay model which would be used to describe the dynamics of sub-surface water reservoir pollution. The results from the validation of the model were analyzed   to determine how time delays in the mixing processes affect the rate of particle movement in water reservoirs.

scholarly journals Design of time-delayed safety switches for CRISPR gene therapy

2021 ◽  
Author(s):  
Dashan Sun
Keyword(s):  
Gene Therapy ◽  
Immune Response ◽  
Time Delay ◽  
Cell Lines ◽  
Gene Editing ◽  
Drug Accumulation ◽  
Work Time ◽  
Crispr System ◽  
Efficient Gene ◽  
Target Effect

CRISPR system is a powerful gene editing tool which has already been reported to address a variety of gene relevant diseases in different cell lines. However, off-target effect and immune response caused by Cas9 remain two fundamental problems. In our work, time-delayed safety switches are designed based on either artificial ultrasensitivity transmission module or intrinsic time delay in biomolecular activities. By addressing gene therapy efficiency, off-target effect, immune response and drug accumulation, we hope our safety switches may offer inspiration in realizing safe and efficient gene therapy in humans.

MATHEMATICAL MODELING OF IMMUNE-INFLAMMATORY REACTION IN ACUTE PNEUMONIA

1995 ◽  
Vol 03 (02) ◽  
pp. 429-439 ◽  
Author(s):  
S. G. RUDNEV ◽  
A. A. ROMANYUKHA
Keyword(s):  
Mathematical Modeling ◽  
Experimental Data ◽  
Mathematical Model ◽  
Immune Response ◽  
Sensitivity Analysis ◽  
Inflammatory Reaction ◽  
Humoral Immune ◽  
Disease Characteristics ◽  
Acute Pneumonia ◽  
Lung Resistance

Using ordinary differential equations, we propose a mathematical model describing an “averaged” dynamics of variables involved in which some parameters are shown to be important characteristics of lung resistance. The model consists of modified D.A. Lauffenburger’s mathematical model for inflammatory reaction in lungs, and the model of humoral immune response (G. I. Marchuk). Coefficients are identified against clinical and experimental data. We attempt to elucidate some disease characteristics in terms of sensitivity analysis of model solutions with respect to parameters variations.

scholarly journals Decoupling Adaptive Smith Prediction Model of Flatness Closed-Loop Control and Its Application

Processes ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 895
Author(s):  
Mingming Song ◽  
Hongmin Liu ◽  
Yanghuan Xu ◽  
Dongcheng Wang ◽  
Yangyang Huang
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Time Delay ◽  
Control Method ◽  
Delay System ◽  
Control Performance ◽  
Time Delay System ◽  
Single Loop ◽  
Flatness Control ◽  
Pure Time Delay

Flatness control system is characterized by multi-parameters, strong coupling, pure time delay, which complicate the establishment of an accurate mathematical model. Therefore, a control scheme that combines dynamic decoupling, PI (Proportion and Integral) control and adaptive Smith predictive compensation is proposed. To this end, a dynamic matrix is used to decouple the control system. A multivariable coupled pure time-delay system is transformed into several independent generalized single-loop pure time-delay systems. Then, a PI-adaptive Smith predictive controller is constructed for the decoupled generalized single-loop pure time-delay system. Simulations show that the scheme has a simple and feasible structure, and good control performance. When the mathematical model of the control system is inaccurate, the control performance of adaptive Smith control method is evidently better than that of the ordinary Smith control method. The model is successfully applied to the cold rolling production site through LabVIEW, and the control accuracy is within 5I. This study reveals a new solution to the problem of coupled pure time-delay in flatness control system.

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