Stochastic epidemics in a homogeneous community

Britton, Tom; Pardoux, Etienne

doi:10.48550/arxiv.1808.05350

Cited by 5 publications

(9 citation statements)

References 19 publications

(22 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1 N with probability going to 1 conditionally on (T ε < +∞) when N → +∞. This, (10), (12) and the definition of T show that lim inf…”

Section: Propositionmentioning

confidence: 81%

“…The following result provides bounds for population fluctuations over very large time intervals for such initial conditions, which will prove useful to describe the early phase of the epidemic in the next section. Its proof is based on a Freidlin-Wentzelltype results on large deviations from a deterministic approximation given in [39] (see also [29,12]) and can be found in the Appendix. Proposition 3 Let ε ∈ (0, z * ∞ ) and denote by τ N ε the exit time of the ball B ∞ (z * , ε) by X N /N .…”

Section: Proposition 2 Define Z As the Solution Of The Cauchy Problemmentioning

confidence: 99%

See 1 more Smart Citation

A stochastic SIR model on a graph with epidemiological and population dynamics occurring over the same time scale

Montagnon

2019

J. Math. Biol.

View full text Add to dashboard Cite

We define and study an open stochastic SIR (Susceptible -Infected -Removed) model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same time scale. Population transition intensities are assumed to be densitydependent with a constant component, the amplitude of which determines the overall scale of the population process. Standard branching approximation results for the epidemic process are first given, along with a numerical computation method for the probability of a major epidemic outbreak. This procedure is illustrated using real data on trade-related cattle movements from a densely populated livestock farming region in western France (Finistère) and epidemiological parameters corresponding to an infectious epizootic disease. Then we exhibit an exponential lower bound for the extinction time and the total size of the epidemic in the stable endemic case as a scaling parameter goes to infinity using results inspired by the Freidlin-Wentzell theory of large deviations from a dynamical system. Keywords multitype SIR model · epidemic and demography over the same time scale · continuous-time multitype branching processes · Markovian process · major outbreak probability · basic reproduction number · real network · epidemic extinction time · epidemic total size · endemicity

show abstract

“…1 N with probability going to 1 conditionally on (T ε < +∞) when N → +∞. This, (10), (12) and the definition of T show that lim inf…”

Section: Propositionmentioning

confidence: 81%

Section: Proposition 2 Define Z As the Solution Of The Cauchy Problemmentioning

confidence: 99%

A stochastic SIR model on a graph with epidemiological and population dynamics occurring over the same time scale

Montagnon

2019

J. Math. Biol.

View full text Add to dashboard Cite

show abstract

“…Density-dependent Markov chains are widely used, in ecology, biology, chemistry and epidemiology, to model the evolution of populations. Let us cite [1,6,22] for numerous examples, including stochastic Lotka-Volterra models, chemical reaction networks and epidemic models. Such chains record the abundances of a finite set of populations, in interaction with one another.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Strong Gaussian approximation of metastable density-dependent Markov chains on large time scales

Prodhomme

2023

Stochastic Processes and their Applications

View full text Add to dashboard Cite

“…Finally, this analysis relies on numerical results. This enables us to explore the role of stochasticity, which is particularly important to consider in the context of outbreak emergence from a mathematical modelling [14] and a statistical inference [34] point of view. However, it limits our analysis to the area of punctual parameters that we selected as being biologically relevant.…”

Section: Discussionmentioning

confidence: 99%

The source of individual heterogeneity shapes infectious disease outbreaks

Elie

Selinger

Alizon

2021

Preprint

View full text Add to dashboard Cite

It is now common-place that pathogen transmission during an outbreak can be more heterogeneous than what is commonly assumed, and that it can have major consequences on their dynamics. However, previous studies did not explore the impact of the different biological sources of heterogeneity while controlling for the resulting heterogeneity in the number of secondary cases. In this study, we explore the role of individual variation in infection duration and transmission rate on parasite emergence and spread in a population. We simulate outbreaks using a custom stochastic SIR model, with and without evolution of the parasite. We show that for a given mean, the variance in the number of secondary cases is the main driver of the outbreak probability, with or without evolution, while it does not play a role on the outbreak dynamic once it emerged. On the opposite, a smaller and more realistic variance in the infection duration causes a faster outbreak. It is therefore useful to take into consideration more realistic distributions when modelling infectious diseases outbreaks.

show abstract

Stochastic epidemics in a homogeneous community

Abstract: Definition A.7.2. The collection {f n , n ≥ 1} is said to be equicontinuous if for anyNote that when X is compact, equicontinuity and uniform equicontinuity are equivalent.

Cited by 5 publications

References 19 publications

A stochastic SIR model on a graph with epidemiological and population dynamics occurring over the same time scale

A stochastic SIR model on a graph with epidemiological and population dynamics occurring over the same time scale

Strong Gaussian approximation of metastable density-dependent Markov chains on large time scales

The source of individual heterogeneity shapes infectious disease outbreaks

Contact Info

Product

Resources

About