Special Issue "Advances on Uncertainty Quantification: Theory and Modelling"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: 30 September 2020.

Special Issue Editors

Prof. Dr. Juan Carlos Cortés López
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Guest Editor
Department of Applied Mathematics and Institute for Multidisciplinary Mathematics (im2), Universitat Politècnica de València, 46022 Valencia, Spain
Interests: differential equations with randomness; mathematical modelling
Special Issues and Collections in MDPI journals
Prof. Dr. Rafael Villanueva Micó
Website
Guest Editor
Department of Applied Mathematics and Institute for Multidisciplinary Mathematics (im2), Polytechnic University of Valencia, 46022 Valencia, Spain
Interests: uncertainty quantification; mathematical epidemiology

Special Issue Information

Dear Colleagues,

Numerous physical, chemical, and biological phenomena, which are very important for scientistic and technological progress, have been traditionally formulated through mathematical models based on ordinary or partial differential equations, where the data (initial/boundary conditions, source term, and/or coefficients) are expressed by means of numerical values or deterministic functions. Nevertheless, scientists really fix these data from measurements, which are always subject to error. How satisfactory the results obtained from the model will be depends on the quality of these measurements (which can frequently take a lot of time and incur high costs). In addition to measurement errors, we must consider the random character of complex external factors that can affect the system, such as pressure, temperature, and humidity in Meteorology; the composition of the land in Seismology; investor tendency and economical policy of countries and companies in Finance; the environmental and genetical factors in Epidemiology; etc. These circumstances make it more advisable to consider the data as random magnitudes; if what is to be measured is a magnitude functionally independent of others values, it would be better to consider it as a random variable; when a dependency exists with respect to other magnitudes, such as time, space, etc., it would be more advisable to interpret it not as a function but as a stochastic process. The consideration of these facts leads to the reformulation of traditional deterministic models, which, in order to improve them, must be replaced by random models. Thus, this is the main purpose of this Special Issue: to gather contributions addressing new analytic and numerical methods and their applications to nontrivial problems to solve, simulate, and approximate random and stochastic equations in a wide sense (algebraic, difference, differential, integral, etc.). Applications of these equations in the settting of applications are particularly welcome.

Prof. Dr. Juan Carlos Cortés López
Prof. Dr. Rafael Villanueva Micó
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Random and stochastic equations (algebraic, difference, differential, integral, etc.)
  • Random numerics
  • Optimization under uncertainty techniques and modeling
  • Parameters estimation techniques for random and stochastic equations
  • Nonlinear systems with random excitation and perturbation and linearization techniques
  • Control theory with randomness
  • Spectral expansions for random and stochastic equations
  • Random fields and applications
  • Approximation of probability densities for random and stochastic equations
  • Efficient simulation techniques for random and stochastic equations
  • Models with uncertainty in biology, physics, chemistry, economics, and engineering

Published Papers (2 papers)

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Research

Open AccessArticle
Improving Stability Conditions for Equilibria of SIR Epidemic Model with Delay under Stochastic Perturbations
Mathematics 2020, 8(8), 1302; https://doi.org/10.3390/math8081302 - 06 Aug 2020
Abstract
So called SIR epidemic model with distributed delay and stochastic perturbations is considered. It is shown, that the known sufficient conditions of stability in probability of the equilibria of this model, formulated immediately in the terms of the system parameters, can be improved [...] Read more.
So called SIR epidemic model with distributed delay and stochastic perturbations is considered. It is shown, that the known sufficient conditions of stability in probability of the equilibria of this model, formulated immediately in the terms of the system parameters, can be improved by virtue of the method of Lyapunov functionals construction and the method of Linear Matrix Inequalities (LMIs). It is also shown, that stability can be investigated immediately via numerical simulation of a solution of the considered model. Full article
(This article belongs to the Special Issue Advances on Uncertainty Quantification: Theory and Modelling)
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Open AccessFeature PaperArticle
Probabilistic Study of the Effect of Anti-Epileptic Drugs Under Uncertainty: Cost-Effectiveness Analysis
Mathematics 2020, 8(7), 1120; https://doi.org/10.3390/math8071120 - 09 Jul 2020
Abstract
Epilepsy is one of the most ancient diseases. Despite the efforts of scientists and doctors to improve the quality of live of epileptic patients, the disease is still a mystery in many senses. Anti-epileptic drugs are fundamental to reduce epileptic seizures but it [...] Read more.
Epilepsy is one of the most ancient diseases. Despite the efforts of scientists and doctors to improve the quality of live of epileptic patients, the disease is still a mystery in many senses. Anti-epileptic drugs are fundamental to reduce epileptic seizures but it have some adverse effects, which influence the quality of life outcomes of the patients. In this paper, we study the effectiveness of anti-epileptic drugs taking into account the inherent uncertainty. We establish a model, which allows to represent the natural history of epilepsy, using Markov chains. After randomizing the mathematical model, we compute the first probability density function of the solution stochastic process applying the random variable transformation technique. We also take advantage of this method to determine the distribution of some key quantities in medical decision, such as the time until a certain proportion of the population remains in each state and the incremental cost-effectiveness ratio. The study is completed computing all these quantities using data available in the literature. In addition, regarding the incremental cost-effectiveness ratio, different third generation anti-epileptic treatments are compared with the Brivaracetam, a new third generation anti-epileptic drug. Full article
(This article belongs to the Special Issue Advances on Uncertainty Quantification: Theory and Modelling)
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