J.R. Artalejo

Complutense University of Madrid, Madrid, Madrid, Spain

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Publications (101)81.46 Total impact

  • J.R. Artalejo, M.J. Lopez-Herrero
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    ABSTRACT: 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.
    Applied Mathematical Modelling 09/2014; · 2.16 Impact Factor
  • Jesús R. Artalejo, Pilar Moreno
    Asia Pacific Journal of Operational Research 05/2014; 31(02). · 0.30 Impact Factor
  • Jesus R Artalejo
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    ABSTRACT: We analyze the dynamics of nosocomial infections in intensive care units (ICUs) by using a Markov chain model. Since population size in the ICU is small, in contrast to previous studies, we concentrate on the analytical solution rather than using simulation. We investigate how changes in the system parameters affect to some important behavioral indicators of the spread of the pathogen. We also present an exact measure of the number of secondary cases of infection produced by one colonized patient.
    Acta Biotheoretica 10/2013; · 0.95 Impact Factor
  • Julia Amador, Jesus R. Artalejo
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    ABSTRACT: Modeling and understanding virus spreading is a crucial issue in computer security. Epidemiological models have been proposed to deal with this problem. We investigate the dynamics of computer virus spreading by considering an stochastic susceptible-infected-removed-susceptible (SIRS) model where immune computers send warning signals to reduce the propagation of the virus among the rest of the computers in the network. We perform an exhaustive analysis of the main indicators of the spread and persistence of the infection. To this end, we provide a detailed study of the quasi-stationary distribution, the number of cases of infection, the extinction time and the hazard time.
    Journal of the Franklin Institute 06/2013; 350(5):1112–1138. · 2.42 Impact Factor
  • J R Artalejo, M J Lopez-Herrero
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    ABSTRACT: The basic reproduction number, R 0, is probably the most important quantity in epidemiology. It is used to measure the transmission potential during the initial phase of an epidemic. In this paper, we are specifically concerned with the quantification of the spread of a disease modeled by a Markov chain. Due to the occurrence of repeated contacts taking place between a typical infective individual and other individuals already infected before, R 0 overestimates the average number of secondary infections. We present two alternative measures, namely, the exact reproduction number, R e0, and the population transmission number, R p , that overcome this difficulty and provide valuable insight. The applicability of R e0 and R p to control of disease spread is also examined.
    Bulletin of Mathematical Biology 04/2013; · 2.02 Impact Factor
  • Julia Amador, Jesus R. Artalejo
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    ABSTRACT: The aim of this paper is to contribute to the connection between computer viruses spreading and epidemiological models. To this end, the block-structured state-dependent event (BSDE) approach is used to study the number of cases of infection in a computer network. The goal of the BSDE approach is the possibility of dealing with non-exponential models with correlated flows, but keeping tractable the dimensionality of the underlying Markov chain. The obtained results are illustrated by numerical experiments which show how the BSDE approach is helpful to strengthen the computer security when it is used in connection with a warning mechanism. An application to the propagation of the CodeRed-II virus is also included.
    Computer Networks. 01/2013; 57(1):302–316.
  • J.R. Artalejo
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    ABSTRACT: This note provides a unified approach to the distribution of the time to extinction from quasi-stationarity for general Markov chains evolving both in discrete and in continuous time. Our results generalize a number of similar derivations which were established ad hoc for a variety of stochastic epidemic models. On the other hand, the obtained results unify the infinite irreducible case and the finite (reducible or irreducible) case which are typically presented under separate formulations in the literature for Markov chains.
    Physica A: Statistical Mechanics and its Applications 10/2012; 391(19):4483–4486. · 1.68 Impact Factor
  • J R Artalejo, A Economou, M J Lopez-Herrero
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    ABSTRACT: We investigate stochastic [Formula: see text] and [Formula: see text] epidemic models, when there is a random environment that influences the spread of the infectious disease. The inclusion of an external environment into the epidemic model is done by replacing the constant transmission rates with dynamic rates governed by an environmental Markov chain. We put emphasis on the algorithmic evaluation of the influence of the environmental factors on the performance behavior of the epidemic model.
    Journal of Mathematical Biology 08/2012; · 2.37 Impact Factor
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    J R Artalejo, A Economou, M J Lopez-Herrero
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    ABSTRACT: We deal with stochastic epidemic models having a set of absorbing states. The aim of the paper is to study some continuous characteristics of the epidemic. In this sense, we first extend the classical study of the length of an outbreak by investigating the whole probability distribution of the extinction time via Laplace transforms. Moreover, we also study two almost new epidemic descriptors, namely, the time until a non-infected individual becomes infected and the time until the individual is removed from the infective group. The obtained results are illustrated by numerical examples including an application to a stochastic SIS model for head lice infections.
    Journal of Biological Dynamics 03/2012; 6(2):189-211.
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    J. R. Artalejo, Q.-L. Li
    Operational Research. An International Journal. 01/2012; 12(2).
  • J. R. Artalejo, M. J. Lopez-Herrero
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    ABSTRACT: This paper uses the block-structured state-dependent event (BSDE) approach to generalize the scalar version of the single server retrial queue with finite population. The simple scalar version only involves exponential random variables, which make the underlying Markov chain tractable. However, this is a drawback in applications where the exponentiality is not a realistic assumption and the flows are correlated. The BSDE approach provides a versatile tool to deal with a non-exponential model with correlated flows, but keeping tractable the dimensionality of the block-structured Markov chain. We focus on the investigation of the limiting distribution of the system state and the waiting time. The theory is illustrated by numerical experiments, which demonstrate that the proposed BSDE approach can be applied efficiently.
    Operational Research 01/2012;
  • J R Artalejo, M J Lopez-Herrero
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    ABSTRACT: We analyze the dynamics of infectious disease spread by formulating the maximum entropy (ME) solutions of the susceptible-infected-susceptible (SIS) and the susceptible-infected-removed (SIR) stochastic models. Several scenarios providing helpful insight into the use of the ME formalism for epidemic modeling are identified. The ME results are illustrated with respect to several descriptors, including the number of recovered individuals and the time to extinction. An application to infectious data from outbreaks of extended spectrum beta lactamase (ESBL) in a hospital is also considered.
    Theoretical Population Biology 12/2011; 80(4):256-64. · 1.24 Impact Factor
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    Jesus Artalejo,, Tuan Phung-Duc
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    ABSTRACT: The main aim of this paper is to study the steady state behavior of an M/G/1-type retrial queue in which there are two flows of arrivals namely ingoing calls made by regular customers and outgoing calls made by the server when it is idle. We carry out an extensive stationary analysis of the system, including stability condition, embedded Markov chain, steady state joint distribution of the server state and the number of customers in the orbit (i.e., the retrial group) and calculation of the first moments. We also obtain light-tailed asymptotic results for the number of customers in the orbit. We further formulate a more complicate but realistic model where the arrivals and the service time distributions are modeled in terms of the Markovian arrival process (MAP) and the phase (PH) type distribution.
    Applied Mathematical Modelling 08/2011; 37(4):1811--1822. · 2.16 Impact Factor
  • J R Artalejo, A Economou, M J Lopez-Herrero
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    ABSTRACT: 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.
    Mathematical biosciences 11/2010; 228(1):45-55. · 1.30 Impact Factor
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    J R Artalejo, M J Lopez-Herrero
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    ABSTRACT: Many stochastic systems, including biological applications, use Markov chains in which there is a set of absorbing states. It is then needed to consider analogs of the stationary distribution of an irreducible chain. In this context, quasi-stationary distributions play a fundamental role to describe the long-term behavior of the system. The rationale for using quasi-stationary distribution is well established in the abundant existing literature. The aim of this study is to reformulate the ratio of means approach (Darroch and Seneta, 1965, 1967) which provides a simple alternative. We have a two-fold objective. The first objective is viewing quasi-stationarity and ratio of expectations as two different approaches for understanding the dynamics of the system before absorption. At this point, we remark that the quasi-stationary distribution and a ratio of means distribution may give or not give similar information. In this way, we arrive to the second objective; namely, to investigate the possibility of using the ratio of expectations distribution as an approximation to the quasi-stationary distribution. This second objective is explored by comparing both distributions in some selected scenarios, which are mainly inspired in stochastic epidemic models. Previously, the rate of convergence to the quasi-stationary regime is taking into account in order to make meaningful the comparison.
    Journal of Theoretical Biology 09/2010; 266(2):264-74. · 2.35 Impact Factor
  • Jesus R. Artalejo, A. Gómez-Corral
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    ABSTRACT: The literature on queueing systems with state-dependent parameters includes a variety of features, such as finite populations, server vacations, variable service rates, queue length dependence, retrials, and control of the admission upon arrival. The complexity of the stochastic models obtained by combining these non-homogeneous features and the method of stages causes practical difficulties. From the point of view of the numerical implementation, the large dimensionality of the underlying matrix representations is a serious problem that requires attention. Specifically, this is a key aspect if an arbitrary, even infinite number of Markovian arrival processes and phase-type distributions are involved. These considerations on the inherent difficulties associated with the stochastic modeling of block-structured state-dependent (BSDE) Markov chains provide the motivation for our study. In this paper, we briefly present the BSDE approach to construct either a specific part or the whole stochastic system in continuous time, modeling a state-dependent phenomenon operating in the presence of phases. A variant of the approach also holds in discrete time. We focus on the correlation structure and present two measures of correlation between events.
    07/2010;
  • J.R. Artalejo, M.J. Lopez-Herrero
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    ABSTRACT: Many of the currently used cellular networks have been constructed on the premise that the retrial phenomenon is negligible and the operating environment is static. However, a proper modeling of the mobile cellular network cannot ignore the existence of repeated calls. Moreover, real systems often operate in varying environment conditions. In this paper, we show how the matrix-analytic formalism gives one the ability to construct and study versatile cellular mobile networks with user retrials operating in random environment. More concretely, we investigate two four-dimensional Markovian models which allow us to represent two different options for the use of the guard channel concept. We put emphasis on the numerical evaluation of the redial behavior and the environmental factors on the system performance. This implies the performance analysis of a variety of descriptors including blocking probabilities (handover and fresh calls), mean average analysis, and waiting time in orbit.
    Computers & Operations Research 07/2010; 37(7):1158–1166. · 1.91 Impact Factor
  • J.R. Artalejo
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    ABSTRACT: In this work, we present a bibliography on retrial queues which updates the bibliography published in this journal in Artalejo (1999) [7]. The bibliography is focused on the progress made during the last decade 2000–2009. For the sake of completeness, a few papers published in 1999, and non-cited in Artalejo (1999) [7], have also been included. To keep the length manageable we have excluded conference proceedings, theses, unpublished reports, and works in languages other than English.The bibliography is structured in the following way:Section 1 lists the recent specific book (Artalejo and Gomez-Corral (2008)) [1] and other monographs including any chapter or section devoted to retrial queues.Section 2 lists survey papers and bibliographic works.Section 3 lists papers published in scientific journals.Section 4 includes a few forthcoming papers already in press.The author hopes that this bibliography could be of help to anyone contemplating research on retrial queues.
    Mathematical and Computer Modelling 05/2010; · 1.42 Impact Factor
  • Jesús Artalejo, Antonio Gómez-Corral, Qi-Ming He
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    ABSTRACT: From the introduction: This survey paper is aimed on providing information on Markovian arrival processes, putting emphasis on the discussion of extensions and variants of the batch Markovian arrival processes (BMAPs), as well as on the wide use of this class of processes in applications. Following the leads in this paper and the guidance provided by the bibliographical notes, readers can get access to the background materials where technical details and proofs are available. In Section 2, we first introduce the BMAP and the continuous phase type distribution. A number of important particular cases, the basic properties and descriptors of the BMAP, as well as some applications in queueing, reliability and inventory models are presented in subsequent sections. In Section 3, we consider a number of generalizations and variants of the BMAP including the discrete counterpart, the marked Markovian arrival process, the HetSigma approach, the Markov-additive processes of arrivals and the block-structured state-dependent event (BSDE) approach. The consideration of these extensions and variants enriches the methodology and enhances the versatility of the arrival processes in different directions. Based on the fact that the BSDE approach allows us to deal with modulated non-homogeneous settings, but keeping the dimensionality of the underlying matrices tractable, Section 4 applies this approach to the susceptible-infected-susceptible epidemic model. We conclude the survey with a few bibliographical notes.Reviewer: Oleg K. Zakusilo (Kyïv)
    SORT (Statistics and Operations Research Transactions) 01/2010; 2(2). · 0.46 Impact Factor
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    Jesus R. Artalejo, Quan-Lin Li
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    ABSTRACT: In this paper, we introduce a new discrete block state-dependent arrival (D-BSDA) distribution which provides fresh insights leading to a successful generalization of the discrete-time Markovian arrival process (D-MAP). The D-BSDA distribution is related to structured Markov chains and the method of stages. The consideration of this new discrete-time state-dependent block description gives one the ability of construct new stochastic models. The retrial queue analyzed in this paper gives an example of application of the D-BSDA distribution to construct more general and sophisticated models. We assume that the primary arrivals and the retrials follow the D-BSDA description and the service times are of discrete phase-type (PH). We study the underlying level dependent Markov chain of M/G/1-type at the epochs immediately after the slot boundaries. To this end, we employ the UL-type RG-factorization which provides an expression for the stationary probabilities. We also perform an analysis of waiting times. Numerical experiments are presented to study the system performance.
    Discrete Event Dynamic Systems 01/2010; 20:325-347. · 0.71 Impact Factor