Extreme values in SIR epidemic models with two strains and cross-immunity

The paper explores the dynamics of extreme values in an SIR (susceptible → infectious → removed) epidemic model with two strains of a disease. The strains are assumed to be perfectly distinguishable, instantly diagnosed and each strain of the disease confers immunity against the second strain, thus showing total cross-immunity. The aim is to derive the joint probability distribution of the maximum number of individuals simultaneously infected during an outbreak and the time to reach such a maximum number for the first time. Specifically, this distribution is analyzed by distinguishing between a global outbreak and the local outbreaks, which are linked to the extinction of the disease and the extinction of particular strains of the disease, respectively. Based on the mass function of the maximum number of individuals simultaneously infected during the outbreak, we also present an iterative procedure for computing the final size of the epidemic. For illustrative purposes, the twostrain SIR-model with cross-immunity is applied to the study of the spread of antibiotic-sensitive and antibiotic-resistant bacterial strains within a hospital ward

Markovian arrivals in stochastic modelling: a survey and some new results

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, nonhomogeneous 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.Peer Reviewe

Markovian arrivals in stochastic modelling : a survey and some new results

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, nonhomogeneous 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

Simulación de datos para predicción de eventos extremos

Ponencia donde se presenta el Grupo de Modelos Estocásticos, sus contribuciones a los modelos y las nuevas líneas de investigación en desarrollo: 1. Modelos de epidemias con vacunación, 2. Modelos de epidemias con multiples tipos de infección, 3. Métodos inspirados en teoría de colas y procesos relacionados aplicados a epidemias, 4. Inferencia en modelos de epidemias y 5. Movilidad y transferencia de resultados.N

A structured Markov chain model to investigate the effects of pre-exposure vaccines in tuberculosis control

In this paper, the interest is in a structured Markov chain model to describe the transmission dynamics of tuberculosis (TB) in the setting of small communities of hosts sharing confined spaces, and to explore the potential impact of new pre-exposure vaccines on reducing the number of new TB cases during an outbreak of the disease. The model under consideration incorporates endogenous reactivation of latent tubercle bacilli, exogenous reinfection of latently infected TB hosts, loss of effectiveness of the vaccine protection, and death of hosts due to tubercle bacilli and from causes beyond TB. Various probabilistic measures are defined and analytically studied to describe extreme values and the number of vaccinations during an outbreak, and a random version of the basic reproduction number is used to measure the transmission potential during the initial phase of the epidemic. Our numerical experiments allow us to compare different pre-exposure vaccines versus the level of coverage in terms of these probabilistic measures

A Markov chain model to investigate the spread of antibiotic-resistant bacteria in hospitals

This paper proposes a Markov chain model to describe the spread of a single bacterial species in a hospital ward where patients may be free of bacteria or may carry bacterial strains that are either sensitive or resistant to antimicrobial agents. The aim is to determine the probability law of the exact reproduction number Rexact,0 which is here defined as the random number of secondary infections generated by those patients who are accommodated in a predetermined bed before a patient who is free of bacteria is accommodated in this bed for the first time. Specifically, we decompose the exact reproduction number Rexact,0 into two contributions allowing us to distinguish between infections due to the sensitive and the resistant bacterial strains. Our methodology is mainly based on structured Markov chains and the use of related matrix-analytic methods.Depto. de Estadística e Investigación OperativaFac. de Ciencias MatemáticasFALSEMinisterio de Ciencia e InnovaciónFundação para a Ciência e a Tecnologia (Portugal)unpu

SEM image analysis in permeable recycled concretes with silica fume. A quantitative comparison of porosity and the ITZ

Recycled aggregates (RA) from construction and demolition can be used in permeable concretes (PC), improving the environment. PCs have a significant porous network, their cement paste and the interaction between the paste and the RA establishing their strength. Therefore, it is important to evaluate the porosity in the interfacial transition zones. The porosity of the cement paste, the aggregate and the interfacial transitional zones (ITZ) of a PC with recycled coarse aggregates (RCA) and silica fume (SF) is measured by means of image analysis–scanning electron microscope (IA)-(SEM) and by mapping the chemical elements with an SEM-EDS (energy dispersive spectrometer) detector microanalysis linked to the SEM and, as a contrast, the mercury intrusion porosimetry technique (MIP). In the IA process, a “mask” was created for the aggregate and another for the paste, which determined the porosity percentage (for the anhydrous material and the products of hydration). The results showed that using SF caused a reduction (32%) in the cement paste porosity in comparison with the PC with RA. The use of RA in the PC led to a significant increase (190%) in the porosity at different thicknesses of ITZ compared with the reference PC. Finally, the MIP study shows that the use of SF caused a decrease in the micropores, mesopores and macroporesPeer ReviewedPostprint (published version

A Markov chain model to investigate the spread of antibiotic-resistant bacteria in hospitals

Ordinary differential equation (ODE) models used in mathematical epidemiology assume explicitly or implicitly large populations. For the study of infections in a hospital this is an extremely restrictive assumption as typically a hospital ward has a few dozen, or even fewer, patients. This work reframes a well-known model used in the study of the spread of antibiotic-resistant bacteria in hospitals, to consider the pathogen transmission dynamics in small populations. In this vein, this paper proposes a Markov chain model to describe the spread of a single bacterial species in a hospital ward where patients may be free of bacteria or may carry bacterial strains that are either sensitive or resistant to antimicrobial agents. We determine the probability law of the \emph{exact} reproduction number ${\cal R}_{exact,0}$, which is here defined as the random number of secondary infections generated by those patients who are accommodated in a predetermined bed before a patient who is free of bacteria is accommodated in this bed for the first time. Specifically, we decompose the exact reproduction number ${\cal R}_{exact,0}$ into two contributions allowing us to distinguish between infections due to the sensitive and the resistant bacterial strains. Our methodology is mainly based on structured Markov chains and the use of related matrix-analytic methods. This guarantees the compatibility of the new, finite-population model, with large population models present in the literature and takes full advantage, in its mathematical analysis, of the intrinsic stochasticity.Comment: 30 pages, 9 figure