On the time to reach a critical number of infections in epidemic models with infective and susceptible immigrants

Almaraz, E.; Gómez‐Corral, Antonio; Rodríguez-Bernal, María Teresa

doi:10.1016/j.biosystems.2016.04.007

Cited by 12 publications

(6 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The incidence function is β 2 (s, i) = βsi/N (1 + i 2 ), with β = 5.0 and the limit for resources is I 0 = 5. For a better visualization, distributions are represented for mass points in [2,100], the probability of having a single infectious individual in the outbreak does not depend on the latency rate and its value is 0.287769 according to equation (3). The distribution shows a single mode at (Z = 1) for σ = 1.0 and shows a bimodal shape for σ = 0.00005 or σ = 0.05.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The maximum number of infective in the course of the epidemic is the peak size of the epidemic curve and it gives an idea of how large treatment resources should be with the purpose of keeping demand for facilities around the available amount. In the paper we will compute distributions by following the first-step methodology which produces stable algorithmic results when applied to Markovian compartmental models ( [2], [9]). This methodology is a generalization of the one introduced by Neuts and Li in [32] for the numerical implementation of the final size distribution of the stochastic SIR model.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Cumulative and maximum epidemic sizes for a nonlinear SEIR stochastic model with limited resources

Amador¹,

Lopez-Herrero²

2017

DCDS-B

View full text Add to dashboard Cite

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.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

Cumulative and maximum epidemic sizes for a nonlinear SEIR stochastic model with limited resources

Amador¹,

Lopez-Herrero²

2017

DCDS-B

View full text Add to dashboard Cite

show abstract

“…The analysis of the transmission of an epidemic process has been extended to epidemic models with vector-borne infections (Artalejo 2014), heterogeneous contacts (Economou et al 2015; López-García 2016), infective and susceptible immigrants (Almaraz et al 2016), latency periods (Lopez-Herrero 2017), generally distributed infectious periods (Gómez-Corral and López-García 2017), Markov-modulated interactions (Almaraz and Gómez-Corral 2018) or to models for two-species competition (Gómez-Corral and López-García 2015).…”

Section: Disease Spreadmentioning

confidence: 99%

Measuring Infection Transmission in a Stochastic SIV Model with Infection Reintroduction and Imperfect Vaccine

Gamboa

Lopez-Herrero

2020

Acta Biotheor

View full text Add to dashboard Cite

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 0 , 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 0 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 0 are defined in order to study the influence of the initial coverage and vaccine efficacy on the transmission of the epidemic.

show abstract

“…The objective of Artalejo and López-Herrero [12] is to investigate quasi-stationarity and the ratio of expectations as two conceptually different approaches for understanding the dynamics of the SIR-model and its variant with demography before the extinction of an epidemic. New descriptors, including the time to reach specific numbers of infectives and susceptible individuals [15,Section 3.1], and the time to reach a critical number of infections [15,Section 3.2] are also investigated by using efficient numerical tools; for a related work, see the paper [5] where the interest is in the time to reach a critical number of infections in the SIR-model with infective and susceptible immigrants. Results based on the maximum entropy (ME) formalism are first derived analytically in [13] for the SIR-model, and they are then applied to outbreaks of extended spectrum beta lactamase organisms in intensive care units of hospitals.…”

Section: (Communicated By Gail Wolkowicz)mentioning

confidence: 99%

On SIR-models with Markov-modulated events: Length of an outbreak, total size of the epidemic and number of secondary infections

Almaraz¹,

Gómez‐Corral²

2018

Discrete &Amp; Continuous Dynamical Systems - B

Self Cite

View full text Add to dashboard Cite

A Markov-modulated framework is presented to incorporate correlated inter-event times into the stochastic susceptible-infectious-recovered (SIR) epidemic model for a closed finite community. The resulting process allows us to deal with non-exponential distributional assumptions on the contact process between the compartment of infectives and the compartment of susceptible individuals, and the recovery process of infected individuals, but keeping the dimensionality of the underlying Markov chain model tractable. The variability between SIR-models with distinct level of correlation is discussed in terms of extinction times, the final size of the epidemic, and the basic reproduction number, which is defined here as a random variable rather than an expected value.1. Introduction. The SIR-model is a well-studied epidemic model that, together with its generalizations, has been widely applied to infectious diseases such as measles, chickenpox, or mumps, among other situations where infection confers (typically lifelong) immunity; a good discussion about SIR-models analyzed from deterministic and stochastic perspectives can be found in the lucid texts by Allen [1, 2], Andersson and Britton [8], Bailey [16] and Keeling and Rohani [36]. The SIR-model is first analyzed in depth by Kermack and McKendrick [37] in 1927 in order to study the evolution of a disease in a closed community of finite size where, at time t, individuals are classified into three categories: S(t) susceptibles, I(t) infectives, and R(t) removed individuals. The general description in [37] is related to an homogeneously mixed population (i.e., any infective can infect any susceptible with equal probability), where the infection and recovery rates of a given infective depend on the total time that this individual has been infected for. The analytical

show abstract

On the time to reach a critical number of infections in epidemic models with infective and susceptible immigrants

Cited by 12 publications

References 16 publications

Cumulative and maximum epidemic sizes for a nonlinear SEIR stochastic model with limited resources

Cumulative and maximum epidemic sizes for a nonlinear SEIR stochastic model with limited resources

Measuring Infection Transmission in a Stochastic SIV Model with Infection Reintroduction and Imperfect Vaccine

On SIR-models with Markov-modulated events: Length of an outbreak, total size of the epidemic and number of secondary infections

Contact Info

Product

Resources

About