SIR epidemics driven by Feller processes

Feller processes; final epidemic outcome; martingales; SIR epidemic processes; Statistics and Probability; Mathematics (all); Statistics, Probability and Uncertainty; General Mathematics

Abstract :

[en] We consider a stochastic SIR (susceptible infective removed) model in which the infectious periods are modulated by a collection of independent and identically distributed Feller processes. Each infected individual is associated with one of these processes, the trajectories of which determine the duration of his infectious period, his contamination rate, and his type of removal (e.g. death or immunization). We use a martingale approach to derive the distribution of the final epidemic size and severity for this model and provide some general examples. Next, we focus on a single infected individual facing a given number of susceptibles, and we determine the distribution of his outcome (number of contaminations, severity, type of removal). Using a discrete-time formulation of the model, we show that this distribution also provides us with an alternative, more stable method to compute the final epidemic outcome distribution.

Disciplines :

Mathematics

Author, co-author :

Simon, Matthieu ; Université de Mons - UMONS > Faculté des Science > Service d'Analyse mathématique ; Département de Mathématique, Mons, Belgium

Language :

English

Title :

SIR epidemics driven by Feller processes

Publication date :

02 December 2023

Journal title :

Journal of Applied Probability

ISSN :

0021-9002

Publisher :

Cambridge University Press

Volume :

Issue :

Pages :

1293 - 1316

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0021900223000025

Research unit :

S823 - Analyse mathématique

Research institute :

Complexys

Available on ORBi UMONS :

since 04 January 2024

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