Person:
López Herrero, María Jesús

First Name

María Jesús

Last Name

López Herrero

URI

https://hdl.handle.net/20.500.14352/77420

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Estudios estadísticos

Department

Estadística y Ciencia de los Datos

Area

Estadística e Investigación Operativa

Identifiers

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Now showing 1 - 10 of 11

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
The distribution of the maximum orbit size of an M/G/1 retrial queue during the busy period
(Advances in stochastic modelling, 2002) López Herrero, María Jesús; Neuts, Marcel F.; Artalejo Rodríguez, Jesús Manuel; Krishnamoorthy, A.
In this paper we study the distribution of the maximum orbit size before emptiness in a stable M/G/1 retrial queue. By a recursive scheme, the computation of that distribution is reduced to solving systems of linear equations.
On the exact and population bi-dimensional reproduction numbers in a stochastic SVIR model with imperfect vaccine
(Applied Mathematics and Computation, 2024) Gamboa Pérez, María; López-García, M.; López Herrero, María Jesús; Simos, Theodore E.
We aim to quantify the spread of a direct contact infectious disease that confers permanent immunity after recovery, within a non-isolated finite and homogeneous population. Prior to the onset of the infection and to prevent the spread of this disease, a proportion of individuals was vaccinated. But the administered vaccine is imperfect and can fail, which implies that some vaccinated individuals get the infection when being in contact with infectious individuals. We study the evolution of the epidemic process over time in terms of a continuous-time Markov chain, which represents a general SIR model with an additional compartment for vaccinated individuals. In our stochastic framework, we study two bi-dimensional variables recording infection events, produced by a single infectious individual or by the whole infected group, taking into account if the newly infected individual was previously vaccinated or not. Theoretical schemes and recursive algorithms are derived in order to compute joint probability mass functions and factorial moments for these random variables. We illustrate the applicability of our techniques by means of a set of numerical experiments.
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
The number of inspections until the extinction of an epidemic in a discrete-time stochastic SIS-type model with some applications
(2023) Gamboa Pérez, María; López Herrero, María Jesús
This talk deals with an infective process of type SIS, taking place in a closed population of moderate size that is inspected periodically. Our purpose is to study the extinction time counterpart in discrete-time, that is the random variable that counts the total number of inspections that find an active epidemic process. As the underlying mathematical model involves a discrete-time Markov chain (DTMC) with a single absorbing state, the number of inspections in an outbreak is a first-passage time into this absorbing state. Cumulative probabilities are numerically determined from a recursive algorithm and expected values came from explicit expressions. Additionally, I provide several applications derived from the theoretical results. The talk is based on the paper: Gamboa M. and López-Herrero M.J. (2018). On the number of periodic inspections during outbreaks of discrete-time stochastic SIS epidemic models. Mathematics 6, article 128.DOI: 10.1007/s11538-013- 9836-3
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.
Measuring infection transmission in a stochastic SIV model with infection reintroduction and imperfect vaccine
(Acta Biotheoretica, 2020) Gamboa Pérez, María; López Herrero, María Jesús
An additional compartment of vaccinated individuals is considered in a SIS stochastic epidemic model with infection reintroduction. The quantification of the spread of the disease is modeled by a continuous time Markov chain. A well-known measure of the initial transmission potential is the basic reproduction number R, which determines the herd immunity threshold or the critical proportion of immune individuals required to stop the spread of a disease when a vaccine offers a complete protection. Due to repeated contacts between the typical infective and previously infected individuals, R overestimates the average number of secondary infections and leads to, perhaps unnecessary, high immunization coverage. Assuming that the vaccine is imperfect, alternative measures to R are defined in order to study the influence of the initial coverage and vaccine efficacy on the transmission of the epidemic.
Epidemic transmission on SEIR stochastic models with nonlinear incidence rate
(Mathematical Methods in the Applied Sciences, 2016) López Herrero, María Jesús
Our interest is to quantify the spread of an infective process with latency period and generic incidence rate that takes place in a Önite and homogeneous population. Within a stochastic framework, two random variables are deÖned to describe the variations of the number of secondary cases produced by an index case inside of a closed population. Computational algorithms are presented in order to characterize both random variables. Finally, theoretical and algorithmic results are illustrated by several numerical examples.
Quasi-stationary and ratio of expectations distributions: A comparative study
(Journal of Theoretical Biology, 2010) Artalejo Rodríguez, Jesús Manuel; López Herrero, María Jesús
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.
Cumulative and maximum epidemic sizes for a nonlinear seir stochastic model with limited resources
(Discrete and Continuous Dynamical Systems - Series B (DCDS-B), 2018) Amador Pacheco, Julia; López Herrero, María Jesús; Han, Xiaoying
The paper deals with a stochastic SEIR model with nonlinear incidence rate and limited resources for a treatment. We focus on a long term study of two measures for the severity of an epidemic: The total number of cases of infection and the maximum of individuals simultaneously infected during an outbreak of the communicable disease. Theoretical and computational results are numerically illustrated.