2018
DOI: 10.1016/j.cnsns.2018.04.022
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A nonlinear dynamic age-structured model of e-commerce in spain: Stability analysis of the equilibrium by delay and stochastic perturbations

Abstract: First, we propose a deterministic age-structured epidemiological model to study the diffusion of e-commerce in Spain. Afterwards, we determine the parameters (death, birth and growth rates) of the underlying demographic model as well as the parameters (transmission of the use of ecommerce rates) of the proposed epidemiological model that best fit real data retrieved from the Spanish National Statistical Institute. Motivated by the two following facts: first the dynamics of acquiring the use of a new technology… Show more

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Cited by 14 publications
(4 citation statements)
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“…Appendix A LEMMA A.1 [4]. Let R ∈ R n×n be a positive definite matrix, y = D x(s)μ (ds), where y, x(s) ∈ R n , and μ(ds) is some measure on D such that μ(D) < ∞.…”
Section: Discussionmentioning
confidence: 99%
“…Appendix A LEMMA A.1 [4]. Let R ∈ R n×n be a positive definite matrix, y = D x(s)μ (ds), where y, x(s) ∈ R n , and μ(ds) is some measure on D such that μ(D) < ∞.…”
Section: Discussionmentioning
confidence: 99%
“…It is shown that the investigated equation includes a lot of different very popular in research mathematical models such as Mackey–Glass model, 2‐4 neoclassical growth model, 5‐11 Nicholson's blowflies equation, 4,12‐17 mosquito 18,19 and glassy‐winged sharpshooter populations, 20,21 e‐commerce model, 22‐24 SIR epidemic model, 1,25‐27 some social epidemics models, 1,28,29 model of viral dynamics, 30,31 and many similar others which can be considered as particular cases of the investigated here nonlinear equation.…”
Section: Introductionmentioning
confidence: 99%
“…Recently, more and more attention has been paid to the study of optimal control. (see [12,[24][25][26][27][28][29][30][31] …and references cited There).…”
Section: Introductionmentioning
confidence: 99%