Sensitivity analysis of search area determination mathematical model

2006 ◽  
pp. 1497-1501
Author(s):  
Z Burciu
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Search Area ◽  
Area Determination

SENSITIVITY ANALYSIS AND IDENTIFIABILITY OF A MATHEMATICAL MODEL OF A CHEMICAL REACTION

2021 ◽  
pp. 14-18
Author(s):  
Л.Ф. Сафиуллина
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Numerical Calculations ◽  
Specific Reaction ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Kinetics Of

В статье рассмотрен вопрос идентифицируемости математической модели кинетики химической реакции. В процессе решения обратной задачи по оценке параметров модели, характеризующих процесс, нередко возникает вопрос неединственности решения. На примере конкретной реакции продемонстрирована необходимость проводить анализ идентифицируемости модели перед проведением численных расчетов по определению параметров модели химической реакции. The identifiability of the mathematical model of the kinetics of a chemical reaction is investigated in the article. In the process of solving the inverse problem of estimating the parameters of the model, the question arises of the non-uniqueness of the solution. On the example of a specific reaction, the need to analyze the identifiability of the model before carrying out numerical calculations to determine the parameters of the reaction model was demonstrated.

scholarly journals Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Caroline W. Kanyiri ◽  
Kimathi Mark ◽  
Livingstone Luboobi
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Drug Resistance ◽  
Stability Analysis ◽  
Influenza A ◽  
Reproduction Number ◽  
Critical Value ◽  
Backward Bifurcation ◽  
Transmission Dynamics ◽  
High Morbidity

Every year, influenza causes high morbidity and mortality especially among the immunocompromised persons worldwide. The emergence of drug resistance has been a major challenge in curbing the spread of influenza. In this paper, a mathematical model is formulated and used to analyze the transmission dynamics of influenza A virus having incorporated the aspect of drug resistance. The qualitative analysis of the model is given in terms of the control reproduction number,Rc. The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lowerRcto a critical valueRc∗for effective disease control. Sensitivity analysis results reveal that vaccine efficacy is the parameter with the most control over the spread of influenza. Numerical simulations reveal that despite vaccination reducing the reproduction number below unity, influenza still persists in the population. Hence, it is essential, in addition to vaccination, to apply other strategies to curb the spread of influenza.

scholarly journals Fractional-Order Modelling and Optimal Control of Cholera Transmission

2021 ◽  
Vol 5 (4) ◽  
pp. 261
Author(s):  
Silvério Rosa ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Sensitivity Analysis ◽  
Fractional Order ◽  
Control Measures ◽  
Time Interval ◽  
Variable Order ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Derivative Order

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

scholarly journals Sensitivity analysis of the mathematical model of catalytic reforming of gasoline

2019 ◽  
Vol 3 (2) ◽  
pp. 43-53
Author(s):  
L. F. Safiullina ◽  
◽  
I. M. Gubaydullin ◽  
K. F. Koledina ◽  
R. Z. Zaynullin ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Catalytic Reforming ◽  
The Mathematical Model

scholarly journals SIMULATION AND SENSITIVITY ANALYSIS ON THE PARAMETER OF NON-TARGETED IRRADIATION EFFECTS MODEL

2018 ◽  
Vol 81 (1) ◽  
Author(s):  
Muhamad Hanis Nasir ◽  
Fuaada Mohd Siam
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Real Life ◽  
Double Strand Breaks ◽  
Signal Molecules ◽  
Danger Signal ◽  
Survival Fraction ◽  
Strand Breaks ◽  
Radiation Induced ◽  
The Mathematical Model

Real-life situations showed damage effects on non-targeted cells located in the vicinity of an irradiation region, due to danger signal molecules released by the targeted cells. This effect is widely known as radiation-induced bystander effects (RIBE). The purpose of this paper is to model the interaction of non-targeted cells towards bystander factors released by the irradiated cells by using a system of structured ordinary differential equations. The mathematical model and its simulations are presented in this paper. In the model, the cells are grouped based on the number of double-strand breaks (DSBs) and mis-repair DSBs because the DSBs are formed in non-targeted cells. After performing the model's simulations, the analysis continued with sensitivity analysis. Sensitivity analysis will determine which parameter in the model is the most sensitive to the survival fraction of non-targeted cells. The proposed mathematical model can explain the survival fraction of non-targeted cells affected by the bystander factors.

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.

Global sensitivity analysis in a mathematical model of the renal insterstitium

2017 ◽  
Vol 10 (4) ◽  
pp. 625-649
Author(s):  
Mariel Bedell ◽  
Yilin Lin ◽  
Emmie Román-Meléndez ◽  
Ioannis Sgouralis
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Global Sensitivity Analysis ◽  
Global Sensitivity

Assessing the impact of agrochemicals on schistosomiasis transmission: A mathematical study

2021 ◽  
pp. 2150049
Author(s):  
Liming Cai ◽  
Peixia Yue ◽  
Mini Ghosh ◽  
Xuezhi Li
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Numerical Simulations ◽  
Disease Transmission ◽  
Agricultural Pollution ◽  
Parasitic Disease ◽  
Mathematical Study ◽  
Proposed Model ◽  
Existence And Stability ◽  
The Impact

Schistosomiasis is a snail-borne parasitic disease, which is affecting almost 240 million people worldwide. The number of humans affected by schistosomiasis is continuously increasing with the rise in the use of agrochemicals. In this paper, a mathematical model is formulated and analyzed to assess the effect of agrochemicals on the transmission of schistosomiasis. The proposed model incorporates the effects of fertilizers, herbicides and insecticides on susceptible snails and snail predators along with schistosomiasis disease transmission. The existence and stability of the equilibria in the model are discussed. Sensitivity analysis is performed to identify the key parameters of the proposed model, which contributes most in the transmission of this disease. Numerical simulations are also performed to assess the impact of fertilizers, herbicides and insecticides on schistosomiasis outbreaks. Our study reveals that the agricultural pollution can enhance the transmission intensity of schistosomiasis, and in order to prevent the outbreak of schistosomiasis, the use of pesticides should be controlled.

scholarly journals Parameter sensitivity analysis on a mathematical model of reepithelialization

2019 ◽  
Vol 5 (1) ◽  
pp. 81-84
Author(s):  
Jacquelyn Dawn Parente ◽  
Knut Möller ◽  
Bala Amala Kannan ◽  
Sabine Hensler ◽  
Claudia Kuhlbach ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Wound Healing ◽  
Chronic Wounds ◽  
Parameter Sensitivity ◽  
Parameter Sensitivity Analysis ◽  
Adhesion Coefficient ◽  
Optimal Distance ◽  
Parameter Values

AbstractReepithelialization is the single requirement to define a wound as healed when the barrier function of the skin is restored. An existing reepithelialization mathematical model (RM) simulates wound healing in vitro. This work performs a parameter sensitivity analysis on an existing RM to see how robust the model is for changing wound healing rates for application to chronic wounds (inhibition) and wound healing therapies (activation). The existing RM balances the optimal distance between cells and basal membrane segments (BMs) according to the calculation of intercellular pressure and adhesion force. The RM mimics cell behavior and their interaction by passive migration, which is the displacement of cells from its initial position. First, this work reproduces the RM. The initial case recreates the interaction of a cell with its surrounding cells, while the second case recreates the interaction of the cell with its nearest BMs. These two cases were implemented in MATLAB to estimate optimal distance, intercellular pressure, an adhesive force between cells and the BMs. The analysis computes movement vectors and new positions of each cell at different time steps. Parameter sensitivity analysis was then conducted on the adhesion coefficient, where the original value in the RM was unknown. The results obtained at the assumed original parameter values are similar to the existing RM. As a result of the parameter sensitivity analysis, increasing the adhesion coefficient increases cell movement. High basal adhesion causes passive movement of cells, which in the simulation results is seen as a cellular movement towards wound closure. The existing RM is robust to changing adhesion coefficient values which change the rate of the advancing reepithelialization front. Future work includes fitting adhesion coefficient parameter values to an in vitro wounded tissue visualized by live dyes in treatment therapy experiments.

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