Person:
Artalejo Rodríguez, Jesús Manuel

First Name

Jesús Manuel

Last Name

Artalejo Rodríguez

URI

https://hdl.handle.net/20.500.14352/82709

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Matemáticas

Area

Estadística e Investigación Operativa

Identifiers

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Now showing 1 - 10 of 14

Stochastic epidemic models: new behavioral indicators of the disease spreading
(Applied Mathematical Modelling, 2014) Artalejo Rodríguez, Jesús Manuel; López Herrero, María Jesús
The purpose of this paper is to propose new indicators of the dynamics of infectious disease spread in stochastic epidemic models, including both global system-oriented descriptors (e.g. the final size measured as the number of individuals infected on a least one occasion during an outbreak) and individual-oriented descriptors (e.g. the time to reach an individual run of infections). We focus on birth-and-death models and the basic SIR epidemic model but the methodology remains valid for other nonlinear stochastic epidemic models. The theory is illustrated by numerical experiments which demonstrate that the proposed behavioral indicators can be applied efficiently
Markovian arrivals in stochastic modelling: a survey and some new results
(Sort: Statistics and Operations Research Transactions, 2010) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, Antonio; Qi-Ming, He
This paper aims to provide a comprehensive review on Markovian arrival processes (MAPs), which constitute a rich class of point processes used extensively in stochastic modelling. Our starting point is the versatile process introduced by Neuts (1979) which, under some simplified notation, was coined as the batch Markovian arrival process (BMAP). On the one hand, a general point process can be approximated by appropriate MAPs and, on the other hand, the MAPs provide a versatile, yet tractable option for modelling a bursty flow by preserving the Markovian formalism. While a number of well-known arrival processes are subsumed under a BMAP as special cases, the literature also shows generalizations to model arrival streams with marks, non-homogeneous settings or even spatial arrivals. We survey on the main aspects of the BMAP, discuss on some of its variants and generalizations, and give a few new results in the context of a recent state-dependent extension.
The stochastic SEIR model before extinction: computational approaches
(Applied Mathematics and Computation, 2015) Artalejo Rodríguez, Jesús Manuel; Economou, A.; López Herrero, María Jesús
We study a stochastic epidemic model of Susceptible-Exposed-Infective-Removed (SEIR) type and we quantify its behavior during an outbreak. More specifically, we model the epidemic by a continuous-time Markov chain and we develop efficient computational procedures for the distribution of the duration of an outbreak. We also study the evolution of the epidemic before its extinction using the ratio-of-expectations (RE) distribution for the number of individuals in the various classes of the model. The obtained results are illustrated by numerical examples including an application to an outbreak of Marburg hemorrhagic fever
Mean Value Analysis Of Single Server Retrial Queues
(Asia-Pacific Journal of Operational Research, 2010) Artalejo Rodríguez, Jesús Manuel; Resing, J.A.C.
Mean value analysis is an elegant tool for determining mean performance measures in queueing models. In this paper we show how mean value analysis can be applied to retrial queues. First, we illustrate the technique for the standard M/G/1 retrial queue with exponential retrial times. After that we show how the relations can be adapted to obtain mean performance measures in more advanced M/G/1-type retrial queues.
Stochastic descriptors to study the fate and potential of naive T cell clonotypes in the periphery
(Journal of Mathematical Biology, 2016) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, Antonio; López-García, M.; Molina París, C.
The population of naive T cells in the periphery is best described by determining both its T cell receptor diversity, or number of clonotypes, and the sizes of its clonal subsets. In this paper, we make use of a previously introduced mathematical model of naive T cell homeostasis, to study the fate and potential of naive T cell clonotypes in the periphery. This is achieved by the introduction of several new stochastic descriptors for a given naive T cell clonotype, such as its maximum clonal size, the time to reach this maximum, the number of proliferation events required to reach this maximum, the rate of contraction of the clonotype during its way to extinction, as well as the time to a given number of proliferation events. Our results show that two fates can be identified for the dynamics of the clonotype: extinction in the short-term if the clonotype experiences too hostile a peripheral environment, or establishment in the periphery in the long-term. In this second case the probability mass function for the maximum clonal size is bimodal, with one mode near one and the other mode far away from it. Our model also indicates that the fate of a recent thymic emigrant (RTE) during its journey in the periphery has a clear stochastic component, where the probability of extinction cannot be neglected, even in a friendly but competitive environment. On the other hand, a greater deterministic behaviour can be expected in the potential size of the clonotype seeded by the RTE in the long-term, once it escapes extinction.
On a single server queue with negative arrivals and request repeated
(Journal of Applied Probability, 1999) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, Antonio
There is a growing interest in queueing systems with negative arrivals; i.e. where the arrival of a negative customer has the effect of deleting some customer in the queue. Recently, Hanison and Pitel (1996) investigated the queue length distribution of a single server queue of type M/G/1 with negative arrivals. In this paper we extend the analysis to the context of queueing systems with request repeated. We show that the Limiting distribution of the system state can still be reduced to a Fredholm integral equation. We solve such an equation numerically by introducing an auxiliary 'truncated' system which can easily be evaluated with the help of a regenerative approach.
Performance analysis of a single-server queue with repeated attempts
(Mathematical and Computer Modelling, 1999) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, Antonio
This paper is concerned with the performance evaluation of a single-server queue with repeated attempts and disasters. Our queueing system is characterized by the phenomenon that a customer who finds the server busy upon arrival joins a group of unfilled customers called 'orbit' and repeats his request after some random time. In addition, we consider in this paper the possibility of disasters. When a disaster occurs, all the work (and therefore customers) in the system is destroyed immediately. Our queueing system can be used to model the behaviour of a buffer in computers with virus infections.
A state-dependent Markov-modulated mechanism for generating events and stochastic models
(Mathematical Methods in the Applied Sciences, 2010) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, Antonio
In this paper, we introduce a versatile block-structured state-dependent event (BSDE) approach that provides a methodological tool to construct non-homogeneous Markov-modulated stochastic models. Alternatively, the BSDE approach can be used to construct even a part (e.g. the arrival process) of the model. To illustrate the usefulness of the BSDE approach, several arrival patterns as well as queueing and epidemic models are considered. In particular, we deal with a state-dependent quasi-birth-and-death process that gives a constructive generalization of the scalar birth-and-death process and the homogeneous quasi-birth-and-death process.
Information theoretic analysis for queueing systems with quasi-random input
(Mathematical and Computer Modelling, 1995) Artalejo Rodríguez, Jesús Manuel; Gómez-Corral, Antonio
In this paper, information theoretic inference methodology for system modeling is applied to estimate the stationary distribution for the number of customers in single server queueing systems with service capacity utilized by a finite population. The customers demand i.i.d. service times. Three different models are considered. In Model I, a customer who finds the server busy can be queued, whereas in Models II and III, any customer finding the server busy upon arrival will make repeated attempts to enter service until he eventually finds the server free. Models II and III differ in the retrial policy. Numerical examples illustrate the accuracy of the proposed maximum entropy estimation when it is compared with the classical analysis.
On the number of recovered individuals in the SIS and SIR stochastic epidemic models
(Mathematical Biosciences, 2010) Artalejo Rodríguez, Jesús Manuel; Economou, A.; López Herrero, María Jesús
The basic models of infectious disease dynamics (the SIS and SIR models) are considered. Particular attention is paid to the number of infected individuals that recovered and its relationship with the final epidemic size. We investigate this descriptor both until the extinction of the epidemic and in transient regime. Simple and efficient methods to obtain the distribution of the number of recovered individuals and its moments are proposed and discussed with respect to the previous work. The methodology could also be extended to other stochastic epidemic models. The theory is illustrated by numerical experiments, which demonstrate that the proposed computational methods can be applied efficiently. in particular, we use the distribution of the number of individuals removed in the SIR model in conjunction with data of outbreaks of ESBL observed in the intensive care unit of a Spanish hospital.