Sensitivity Analysis Of Mathematical Model Research Articles

Sensitivity Analysis of Mathematical Models

The construction of a mathematical model of a complicated system is often associated with the evaluation of inputs’ (arguments, factors) influence on the output (response), the identification of important relationships between the variables used, and reduction of the model by decreasing the number of its inputs. These tasks are related to the problems of Sensitivity Analysis of mathematical models. The author proposes an alternative approach based on applying Analysis of Finite Fluctuations that uses the Lagrange mean value theorem to estimate the contribution of changes to the variables of a function to the output change. The article investigates the presented approach on an example of a class of fully connected neural network models. As a result of Sensitivity Analysis, a set of sensitivity measures for each input is obtained. For their averaging, it is proposed to use a point-and-interval estimation algorithm using Tukey’s weighted average. The comparison of the described method with the computation of Sobol’s indices is given; the consistency of the proposed method is shown. The computational robustness of the procedure for finding sensitivity measures of inputs is investigated. Numerical experiments are carried out on the neuraldat data set of the NeuralNetTools library of the R data processing language and on data of the healthcare services provided in the Lipetsk region.

Multi-method global sensitivity analysis of mathematical models

Increasingly-sophisticated parameter-sensitivity analysis techniques continue to be developed, and each technique comes with its own set of advantages and disadvantages. Selecting which parameter-sensitivity method to use for a particular model, however, is not a straightforward task. In this work, we present a multi-method framework that incorporates three global sensitivity analysis methods: two variance-based methods and one derivative-based method. The two variance-based methods are Sobol’s method and MeFAST. The derivative-based method is known as DGSM (Derivative-based Global Sensitivity Measures). MeFAST (Multi test eFAST) is a new parameter sensitivity analysis implementation we built upon the eFAST (Extended Fourier Amplitude Sensitivity Test) algorithm. The improvements incorporated into MeFAST address some important aspects of prior eFAST implementations. We present an intuitive description of each implemented algorithm along with MATLAB codes and a guide to tuning algorithm hyper-parameters for better efficiency. We demonstrate the full methodology and workflow using two example mathematical models of different complexity: the first is a model of HIV disease progression and the second is a model of tumor growth. The computational framework we provide generates graphics for visualizing and comparing the results of all three sensitivity analysis algorithms (DGSM, Sobol, and MeFAST). This algorithm output comparison tool allows one to make a more informed decision when assessing which parameters most importantly influence model outcomes.

A State-of-the-art Model of Location, Inventory, and Pricing Problem in the Closed-loop Supply Chain Network

The main objective of designing the supply chain is to increase profitability. For this reason, a state-of-the-art model of a three-echelon closed-loop supply chain is proposed that consists of the manufacturer, retailer, and collection centers. For the first time, a new separate and autonomous channel is considered in this model for the sale of Reman products aiming at increasing the manufacturer's profitability. In this model, location, inventory, and pricing of the product are also taken into consideration. Lingo software is utilized to solve nonlinear objective functions at a small scale, and metaheuristic genetic algorithms and particle swarm optimization were utilized to solve at a large scale. The research results depict that the state-of-the-art model design of the closed-loop supply chain network is credible and the optimal location of supply chain components, optimal response of product flow, and product price are determined in a proper manner. As a result, the profitability of the whole closed-loop supply chain network increased. Sensitivity analysis of mathematical model depicts that this model shows higher sensitivity to retailer replacement factor, price and purchasing power of collection centers. Also, the genetic algorithm shows better performance on a large scale in terms of response quality. On the other hand, the time required by particle swarm optimization to reach a response is far better than the genetic algorithm. Ultimately, practical suggestions for the managers are presented considering the state-of-the-art model design of a closed-loop supply chain network.

Strength and strain modeling of CFRP-confined concrete cylinders using ANNs

Carbon fiber reinforced polymer (CFRP) has extensive use in strengthening reinforced concrete structures due to its high strength and elastic modulus, low weight, fast and easy application, and excellent durability performance. Many studies have been carried out to determine the performance of the CFRP confined concrete cylinder. Although studies about the prediction of confined compressive strength using ANN are in the literature, the insufficiency of the studies to predict the strain of confined concrete cylinder using ANN, which is the most appropriate analysis method for nonlinear and complex problems, draws attention. Therefore, to predict both strengths and also strain values, two different ANNs were created using an extensive experimental database. The strength and strain networks were evaluated with the statistical parameters of correlation coefficients (R2), root mean square error (RMSE), and mean absolute error (MAE). The estimated values were found to be close to the experimental results. Mathematical equations to predict the strength and strain values were derived using networks prepared for convenience in engineering applications. The sensitivity analysis of mathematical models was performed by considering the inputs with the highest importance factors. Considering the limit values obtained from the sensitivity analysis of the parameters, the performances of the proposed models were evaluated by using the test data determined from the experimental database. Model performances were evaluated comparatively with other analytical models most commonly used in the literature, and it was found that the closest results to experimental data were obtained from the proposed strength and strain models.

Sensitivity Analysis of Mathematical Model to Study the Effect of T Cells Infusion in Treatment of CLL

In this paper, we considered a mathematical model concerned with the treatment of Chronic Lymphocytic Leukemia (CLL) taking into account the effect of superficially infused T cells in this particular type of tumor. The model is described thoroughly by the system of non-linear differential equations explaining the interaction of naïve, infected, cancer and immune cell population. The detailed sensitivity analysis with the application is the major part of this paper. The basic objective is to provide insight to how parameters’ behavior varies model results by elaborating the results obtained from the application of sensitivity analysis. The sensitivity of the model was evaluated not only theoretically, but also with the help of a numerical approach, producing graphs providing better imminent of results. We argue that the application of the sensitivity analysis method endows an insight into how and which parameters are of primary significance in controlling the spread of leukemia.

Sensitivity Analysis of Mathematical Model for Malaria Transmission with Saturated Incidence Rate

Sensitivity Analysis of Mathematical Model for Malaria Transmission with Saturated Incidence Rate

The Determination of Feasible Control Variables for Geoengineering and Weather Modification Based on the Theory of Sensitivity in Dynamical Systems

Geophysical cybernetics allows for exploring weather and climate modification (geoengineering) as an optimal control problem in which the Earth’s climate system is considered as a control system and the role of controller is given to human operators. In mathematical models used in climate studies control actions that manipulate the weather and climate can be expressed via variations in model parameters that act as controls. In this paper, we propose the “instability-sensitivity” approach that allows for determining feasible control variables in geoengineering. The method is based on the sensitivity analysis of mathematical models that describe various types of natural instability phenomena. The applicability of this technique is illustrated by a model of atmospheric baroclinic instability since this physical mechanism plays a significant role in the general circulation of the atmosphere and, consequently, in climate formation. The growth rate of baroclinic unstable waves is taken as an indicator of control manipulations. The information obtained via calculated sensitivity coefficients is very beneficial for assessing the physical feasibility of methods of control of the large-scale atmospheric dynamics and for designing optimal control systems for climatic processes. It also provides insight into potential future changes in baroclinic waves, as a result of a changing climate.

SensA: web-based sensitivity analysis of SBML models.

Summary: SensA is a web-based application for sensitivity analysis of mathematical models. The sensitivity analysis is based on metabolic control analysis, computing the local, global and time-dependent properties of model components. Interactive visualization facilitates interpretation of usually complex results. SensA can contribute to the analysis, adjustment and understanding of mathematical models for dynamic systems.Availability and implementation: SensA is available at http://gofid.biologie.hu-berlin.de/ and can be used with any modern browser. The source code can be found at https://bitbucket.org/floettma/sensa/ (MIT license)Contact: max.floettmann@biologie.hu-berlin.de or thomas.spiesser@biologie.hu-berlin.de

Sensitivity analysis of mathematical models for final product properties: Link to DTG curve

Abstract Compressive strength and water absorption of fired heavy clay products varies with firing temperatures, but not entirely according to linear function, as it is mostly reported in literature. Also, differential thermo-gravimetric curve shows many turnovers in all the samples tested, within observed temperature range (820–920 °C). The aim of this research was to find a cause for such behaviour. Except derivative weight ( DW ), compressive strength ( CS ) and water absorption ( WA ) are chosen as outputs that represent properties of the fired samples. These parameters can be calculated using second order polynomial models (SOPs), on the basis of content of major oxides and firing temperature, as shown in our previous research. Sensitivity analysis was used as the effective approach in testing changes observed in the SOP outputs, due to the variation of content of major oxides for +1% or −1% of their nominal value. This study reveals in more detail the most significant influence of inputs (SiO 2 , Al 2 O 3 , Fe 2 O 3 and CaO content) over the outputs ( DW , CS and WA ) in every observed firing temperature. Addition or lowering of content of major oxides can both increase and decrease all the observed outputs, as revealed using sensitivity analysis.

RESEARCH PAPER Sensitivity analysis of mathematical models of signaling pathways

RESEARCH PAPER Sensitivity analysis of mathematical models of signaling pathways

Sensitivity analysis for dynamic systems with time-lags

Many problems in bioscience for which observations are reported in the literature can be modelled by suitable functional differential equations incorporating time-lags (other terminology: delays) or memory effects, parameterized by scientifically meaningful constant parameters p or/and variable parameters (for example, control functions) u (t) . It is often desirable to have information about the effect on the solution of the dynamic system of perturbing the initial data, control functions, time-lags and other parameters appearing in the model. The main purpose of this paper is to derive a general theory for sensitivity analysis of mathematical models that contain time-lags. In this paper, we use adjoint equations and direct methods to estimate the sensitivity functions when the parameters appearing in the model are not only constants but also variables of time. To illustrate the results, the methodology is applied numerically to an example of a delay differential model.