Advances in Applied Probability

State space collapse for critical multistage epidemics

Florian Simatos

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Abstract

We study a multistage epidemic model which generalizes the SIR model and where infected individuals go through K ≥ 1 stages of the epidemic before being removed. An infected individual in stage k ∈ {1, . . ., K} may infect a susceptible individual, who directly goes to stage k of the epidemic; or it may go to the next stage k + 1 of the epidemic. For this model, we identify the critical regime in which we establish diffusion approximations. Surprisingly, the limiting diffusion exhibits an unusual form of state space collapse which we analyze in detail.

Article information

Source
Adv. in Appl. Probab., Volume 47, Number 3 (2015), 715-740.

Dates
First available in Project Euclid: 8 October 2015

Permanent link to this document
https://projecteuclid.org/euclid.aap/1444308879

Digital Object Identifier
doi:10.1239/aap/1444308879

Mathematical Reviews number (MathSciNet)
MR3406605

Zentralblatt MATH identifier
1334.60124

Subjects
Primary: 60F17: Functional limit theorems; invariance principles

Keywords
Multistage epidemic state space collapse scaling limits

Citation

Simatos, Florian. State space collapse for critical multistage epidemics. Adv. in Appl. Probab. 47 (2015), no. 3, 715--740. doi:10.1239/aap/1444308879. https://projecteuclid.org/euclid.aap/1444308879


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