The dynamics over the next few years of the Spanish mobile telecommunications market share: a mathematical modelling approach

Cervelló, Roberto; López, Juan Carlos Cortés; Santonja, Francisco-José; Micó, Rafael Jacinto Villanueva

doi:10.1080/13873954.2013.843572

Cited by 6 publications

(1 citation statement)

References 11 publications

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“…The importance of contacts in non-infectious phenomena, where the bad-habit group is a "transmitter", has also been revealed within alcohol and tobacco consumption, for example [15,23]. For phenomena not related to health, for example the mobile telecommunications market share [24], contacts and imitation are key too.…”

Section: Introductionmentioning

confidence: 99%

Modeling of adulthood obesity in Spain using Itô-type stochastic differential equations

Calatayud

Jornet

2021

Chaos, Solitons & Fractals

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Section: Introductionmentioning

confidence: 99%

Modeling of adulthood obesity in Spain using Itô-type stochastic differential equations

Calatayud

Jornet

2021

Chaos, Solitons & Fractals

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Spatial modeling of crime dynamics: Patch and reaction–diffusion compartmental systems

Calatayud

Jornet

Mateu

2023

Math Methods in App Sciences

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We study the dynamics of abstract models for crime evolution. The population is divided into three compartments, taking into account the participation in crime and incarceration. Individuals transit between the three segments, assuming that having more contact with criminally active people increases one's risk of learning and acquiring the same traits; essentially, crime is regarded as a social epidemic. In the literature, there are several models of this type, based on spatial homogeneity and ordinary differential equations. However, these ideas have not been extended to account for spatial variability. Here, we achieve this target with discrete and continuous forms of space: patch and reaction–diffusion compartmental systems, respectively. We build the models and focus on the effect of the basic reproduction number on the long‐term dynamics of crime (persistence or disappearance). Several theoretical results are presented, which are supported by numerical simulations.

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Power-series solutions of fractional-order compartmental models

Jornet

2024

Comp. Appl. Math.

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Compartmental models based on coupled differential equations of fractional order have been widely employed in the literature for modeling. An abstraction of these models is given by a system with polynomial vector field. We investigate the use of power series for solving generic polynomial differential equations in any dimension, with Caputo fractional derivative. As is well known, power series convert a continuous formulation into a discrete system of difference equations, which are easily solved by recursion. The novelty of this paper is that we rigorously prove that the series converge on a neighborhood of the initial instant, which is an analogue of the Cauchy–Kovalevskaya theorem. Besides, these series are proved to be continuous with respect to the fractional index. For applications, a general-purpose symbolic implementation of truncated power series is developed, and its execution is illustrated for the fractional SIR epidemiological model.

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The dynamics over the next few years of the Spanish mobile telecommunications market share: a mathematical modelling approach

Cited by 6 publications

References 11 publications

Modeling of adulthood obesity in Spain using Itô-type stochastic differential equations

Modeling of adulthood obesity in Spain using Itô-type stochastic differential equations

Spatial modeling of crime dynamics: Patch and reaction–diffusion compartmental systems

Power-series solutions of fractional-order compartmental models

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