scholarly journals Sensitivity analysis and the inverse problem in the mathematical modelling of tumor ablation using the interstitial hyperthermia

2020 ◽  
Author(s):  
Marek Paruch
Keyword(s):  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Mathematical Modelling ◽  
Tumor Ablation ◽  
Interstitial Hyperthermia

Calculating prescription rates and addiction probabilities for the four most commonly prescribed opioids and evaluating their impact on addiction using compartment modelling

2021 ◽  
Author(s):  
Samantha R Rivas ◽  
Alex C Tessner ◽  
Eli E Goldwyn
Keyword(s):  
Mental Health ◽  
Substance Abuse ◽  
Sensitivity Analysis ◽  
Drug Abuse ◽  
Mathematical Modelling ◽  
Prescription Opioids ◽  
Health Services Administration ◽  
Combining Data ◽  
Control And Prevention ◽  
Prescription Rates

Abstract In 2016, more than 11 million Americans abused prescription opioids. The National Institute on Drug Abuse considers the opioid crisis a national addiction epidemic, as an increasing number of people are affected each year. Using the framework developed in mathematical modelling of infectious diseases, we create and analyse a compartmental opioid-abuse model consisting of a system of ordinary differential equations. Since $40\%$ of opioid overdoses are caused by prescription opioids, our model includes prescription compartments for the four most commonly prescribed opioids, as well as for the susceptible, addicted and recovered populations. While existing research has focused on drug abuse models in general and opioid models with one prescription compartment, no previous work has been done comparing the roles that the most commonly prescribed opioids have had on the crisis. By combining data from the Substance Abuse and Mental Health Services Administration (which tracked the proportion of people who used or misused one of the four individual opioids) with data from the Centers of Disease Control and Prevention (which counted the total number of prescriptions), we estimate prescription rates and probabilities of addiction for the four most commonly prescribed opioids. Additionally, we perform a sensitivity analysis and reallocate prescriptions to determine which opioid has the largest impact on the epidemic. Our results indicate that oxycodone prescriptions are both the most likely to lead to addiction and have the largest impact on the size of the epidemic, while hydrocodone prescriptions had the smallest impact.

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 Voltammetry: Mathematical modelling and Inverse Problem

2016 ◽  
Vol 157 ◽  
pp. 78-84
Author(s):  
Nikolay Koshev ◽  
Alexander Koshev ◽  
Valentina Kuzina
Keyword(s):  
Inverse Problem ◽  
Mathematical Modelling

Sensitivity Analysis and the Ground-Water Inverse Problem

Ground Water ◽  
1982 ◽  
Vol 20 (6) ◽  
pp. 723-735 ◽  
Author(s):  
Carl D. McElwee
Keyword(s):  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Ground Water

scholarly journals Sensitivity analysis of an inverse problem for the wave equation with caustics

2014 ◽  
Vol 27 (4) ◽  
pp. 953-981 ◽  
Author(s):  
Gang Bao ◽  
Hai Zhang
Keyword(s):  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Wave Equation

scholarly journals Mathematical Modelling of Climate Change and Variability in the Context of Outdoor Ergonomics

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2920
Author(s):  
Sergei Soldatenko ◽  
Alexey Bogomolov ◽  
Andrey Ronzhin
Keyword(s):  
Climate Change ◽  
Sensitivity Analysis ◽  
Energy Balance ◽  
Power Spectrum ◽  
Climate Variability ◽  
Mathematical Modelling ◽  
Surface Temperature ◽  
Climate Models ◽  
Energy Balance Model ◽  
Balance Model

The current climate change, unlike previous ones, is caused by human activity and is characterized by an unprecedented rate of increase in the near-surface temperature and an increase in the frequency and intensity of hazardous weather and climate events. To survive, society must be prepared to implement adaptation strategies and measures to mitigate the negative effects of climate change. This requires, first of all, knowledge of how the climate will change in the future. To date, mathematical modelling remains the only method and effective tool that is used to predict the climate system’s evolution under the influence of natural and anthropogenic perturbations. It is important that mathematics and its methods and approaches have played a vital role in climate research for several decades. In this study, we examined some mathematical methods and approaches, primarily, mathematical modelling and sensitivity analysis, for studying the Earth’s climate system, taking into account the dependence of human health on environmental conditions. The essential features of stochastic climate models and their application for the exploration of climate variability are examined in detail. As an illustrative example, we looked at the application of a low-order energy balance model to study climate variability. The effects of variations in feedbacks and the climate system’s inertia on the power spectrum of global mean surface temperature fluctuations that characterized the distribution of temperature variance over frequencies were estimated using a sensitivity analysis approach. Our confidence in the obtained results was based on the satisfactory agreement between the theoretical power spectrum that was derived from the energy balance model and the power spectrum that was obtained from observations and coupled climate models, including historical runs of the CMIP5 models.

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