Person: Artalejo Rodríguez, Jesús Manuel
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First Name
Jesús Manuel
Last Name
Artalejo Rodríguez
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Area
Estadística e Investigación Operativa
Identifiers
5 results
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Now showing 1 - 5 of 5
Item Stochastic epidemic models: new behavioral indicators of the disease spreading(Applied Mathematical Modelling, 2014) Artalejo Rodríguez, Jesús Manuel; López Herrero, María JesúsThe 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 efficientlyItem The stochastic SEIR model before extinction: computational approaches(Applied Mathematics and Computation, 2015) Artalejo Rodríguez, Jesús Manuel; Economou, A.; López Herrero, María JesúsWe 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 feverItem 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 JesúsThe 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.Item Quasi-stationary and ratio of expectations distributions: A comparative study(Journal of Theoretical Biology, 2010) Artalejo Rodríguez, Jesús Manuel; López Herrero, María JesúsMany 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.Item Evaluating growth measures in an immigration process subject to binomial and geometric catastrophes(Mathematical Biosciences and Engineering, 2007) Artalejo Rodríguez, Jesús Manuel; Economou, A.; López Herrero, María JesúsPopulations are often subject to the effect of catastrophic events that cause mass removal. In particular, metapopulation models, epidemics, and migratory flows provide practical examples of populations subject to disasters (e.g., habitat destruction, environmental catastrophes). Many stochastic models have been developed to explain the behavior of these populations. Most of the reported results concern the measures of the risk of extinction and the distribution of the population size in the case of total catastrophes where all individuals in the population are removed simultaneously. In this paper, we investigate the basic immigration process subject to binomial and geometric catastrophes; that is, the population size is reduced according to a binomial or a geometric law. We carry out an extensive analysis including first extinction time, number of individuals removed, survival time of a tagged individual, and maximum population size reached between two consecutive extinctions. Many explicit expressions are derived for these system descriptors, and some emphasis is put to show that some of them deserve extra attention.