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Extinction and Quasi-Stationarity for Discrete-Time, Endemic SIS and SIR Models

Stochastic discrete-time susceptible--infected--susceptible (SIS) and susceptible--infected--recovered (SIR) models of endemic diseases are introduced and analyzed. For the deterministic, mean-field model, the basic reproductive number R0 determines their global dynamics. If R0≤1, then the frequency of infected individuals asymptotically converges to zero. If R0>1, then the infectious class uniformly persists for all time; conditions for a globally stable, endemic equilibrium are given. In contrast, the infection goes extinct in finite time with a probability of 1 in the stochastic models for all R0 values. To understand the length of the transient prior to extinction as well as the behavior of the transients, the quasi-stationary distributions and the associated mean time to extinction are analyzed using large deviation methods. When R0>1, these mean times to extinction are shown to increase exponentially with the population size N. Moreover, as N approaches ∞, the quasi-stationary distributions are supported by a compact set bounded away from extinction; sufficient conditions for convergence to a Dirac measure at the endemic equilibrium of the deterministic model are also given. In contrast, when R0

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Informasi Detail

Judul Seri

SIAM JOURNAL ON APPLIED MATHEMATICS; Vol.81 No.5 September - October 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 2195 - 2217

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

LARGE DEVIATIONS
INFECTIOUS DISEASES
DISCRETE-TIME SIS MODEL
DISCRETE-TIME SIR MODEL
QUASI-STATIONARY DISTRIBUTIONS
TIMES TO EXTINCTION

Info Detail Spesifik

https://doi.org/10.1137/20M1339015

Pernyataan Tanggungjawab

Sebastian J. Schreiber, Shuo Huang, Jifa Jiang, Hao Wang

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