Stochastic comparisons of mixtures of parametric families in stochastic epidemics

Ortega, Eva; Alonso, Jose Raul Gonzalez; Ortega, Isabel

doi:10.1016/j.mbs.2012.12.006

Cited by 8 publications

(5 citation statements)

References 42 publications

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“…Additionally, 14 discusses the detection of worm spread, with suffeciently detailed deterministic and stochastic models. Several stochastic approaches have also been proposed to analyze dynamics of epidemics, for example, Ortega et al 15 To gain an insight into the stochastic models, the reader can examie the survey on stochastic epidemic models presented in Britton. 16 Mathematics and simulation are effective tools assisting us in almost every field of research, in particular, for building models and substantiating the model results with regard to the theoretical background.…”

Section: Motivations and Related Workmentioning

confidence: 99%

Building epidemic models for living populations and computer networks

Kondakci¹,

Kondakci²

2021

Science Progress

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Accurate modeling of viral outbreaks in living populations and computer networks is a prominent research field. Many researchers are in search for simple and realistic models to manage preventive resources and implement effective measures against hazardous circumstances. The ongoing Covid-19 pandemic has revealed the fact about deficiencies in health resource planning of some countries having relatively high case count and death toll. A unique epidemic model incorporating stochastic processes and queuing theory is presented, which was evaluated by computer simulation using pre-processed data obtained from an urban clinic providing family health services. Covid-19 data from a local corona-center was used as the initial model parameters (e.g. [Formula: see text], infection rate, local population size, number of contacts with infected individuals, and recovery rate). A long–run trend analysis for 1 year was simulated. The results fit well to the current case data of the sample corona center. Effective preventive and reactive resource planning basically depends on accurately designed models, tools, and techniques needed for the prediction of feature threats, risks, and mitigation costs. In order to sufficiently analyze the transmission and recovery dynamics of epidemics it is important to choose concise mathematical models. Hence, a unique stochastic modeling approach tied to queueing theory and computer simulation has been chosen. The methods used here can also serve as a guidance for accurate modeling and classification of stages (or compartments) of epidemics in general.

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Section: Motivations and Related Workmentioning

confidence: 99%

Building epidemic models for living populations and computer networks

Kondakci¹,

Kondakci²

2021

Science Progress

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“…] for all concave functions u. Now, it has been shown in [15] that Bin(n, P ) ≤ cv Bin(n, E[P ]). Because Jensen's inequality states that W ≤ cv E[W ] for any random variable W , we see that Bin(n − 1, p(X)) ≤ cv Bin(n − 1, p) ≤ cv (n − 1)p, which proves that (8) holds when u is concave.…”

Section: Generatementioning

confidence: 99%

A Probabilistic Friendship Network Model

Dizon‐Ross¹,

Ross²

2020

Prob. Eng. Inf. Sci.

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We consider a friendship model in which each member of a community has a latent value such that the probability that any two individuals are friends is a function of their latent values. We consider such questions as does information that i and j are both friends with k make it more likely that i and j are themselves friends. Among other things, we show that for fixed sets S and T, the more friends that i has in S, then the stochastically more friends i has in T. We consider how a variation of the friendship paradox applies to our model. We also study the distribution of the number of friendless individuals in the community and derive a bound on the total variation distance between it and a Poisson with the same mean.

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“…To finish this subsection, we provide some background on the research concerning with the variability ordering of mixture models, using stochastic directional convexity. For random sums, some results can be found in Escudero et al [13], Fernandez-Ponce et al [33], Ortega and Escudero [34] and Ortega, Alonso and Ortega [35], with applications in actuarial science, reliability engineering, and epidemic processes, among others; and for random products in Ortega and Alonso [4], as we mentioned, applied in communication and information systems via biologically inspired models.…”

Section: The Analysis Of Variability Of Mixture Measuresmentioning

confidence: 99%

Recent issues on stochastic directional convexity, and new results on the analysis of systems for communication, information, time scales and maintenance

Ortega

Alonso²

2013

Appl Stoch Models Bus & Ind

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In an earlier reference, we provided a review of the regular, sample path and strong stochastic concepts of stochastic convexity in both univariate and multivariate settings, jointly with most of their applications, and some other new results for analysing communication systems on the basis of biologically inspired models. This article provides a comprehensive discussion about the regular notion of stochastic increasing and directional convexity, denoted by SI DCX introduced by Meester and Shanthikumar for a general partially ordered space. We study the connection of the SI DCX property of X.Â/ for Â taking on values over a sublattice and the optimal solution of a maximization problem with objective function given by the expected value of any increasing convex function of the parameterized random variable X.Â/, as well as the analysis of the variability ordering of the mixture model with correlated parameters. We illustrate these results with the conditions for the SI DCX property of the sojourn time at M=ı=1 processor sharing queues, the arrival time at GI/GI/1-queues; best monitoring scales for the ageing description; the total score for the best selected items in sequential screening; moments of multivariate distributions; Keywords: stochastic directional convexity; processor sharing and GI/GI/1-queues; best monitoring scales; sequential screening; traffic on websites; opportunistic maintenance Motivation and preliminariesThe theory of stochastic convexity has played a prominent role as a framework to analyse the stochastic behaviour of parameterized models in both univariate and multivariate settings. These properties have been applied in areas as diverse as communication systems, queueing systems, manufacturing, scheduling, reliability, biotechnology, hydrology, finance, actuarial science and statistics. Consider a family of parameterized univariate or multivariate random variables fX.Â/jÂ 2 T g over a probability space . ; =; P r/, with T R n with n > 1, being some sublattice. The parameter Â represents a value of a random variable influencing the probability distribution of X.Â/. Regular, sample path and strong stochastic convexity notions have been defined to intuitively describe how the random objects X.Â/ grow convexly (or concavely) concerning their parameters in the univariate case. The univariate notions of stochastic convexity were extended to the multivariate case by means of directionally convex functions, leading to different concepts of stochastic directional convexity [1]. Meester and Shanthikumar [2] extended the notions of stochastic directional convexity formulated by Shaked and Shanthikumar [1] to general partially ordered spaces, concluding that this general theory encompasses the univariate stochastic convexity earlier and at the same time allows one the treatment of multivariate multiparameter families as well as more general random objects and stochastic processes. The concepts that we are going to study in this article are some of those in [2]. The regular stochastic directional conve...

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Stochastic comparisons of mixtures of parametric families in stochastic epidemics

Cited by 8 publications

References 42 publications

Building epidemic models for living populations and computer networks

Building epidemic models for living populations and computer networks

A Probabilistic Friendship Network Model

Recent issues on stochastic directional convexity, and new results on the analysis of systems for communication, information, time scales and maintenance

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