Extinction and recurrence of multi-group SEIR epidemic
Yang, Qingshan and Mao, Xuerong (2013) Extinction and recurrence of multi-group SEIR epidemic. Nonlinear Analysis: Real World Applications, 14 (3). pp. 1434-1456. ISSN 1468-1218 (https://doi.org/10.1016/j.nonrwa.2012.10.007)
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Abstract
In this paper, we consider a class of multi-group SEIR epidemic models with stochastic perturbations. By the method of stochastic Lyapunov functions, we study their asymptotic behavior in terms of the intensity of the stochastic perturbations and the reproductive number R0R0. When the perturbations are sufficiently large, the exposed and infective components decay exponentially to zero whilst the susceptible components converge weakly to a class of explicit stationary distributions regardless of the magnitude of R0R0. An interesting result is that, if the perturbations are sufficiently small and R0≤1R0≤1, then the exposed, infective and susceptible components have similar behaviors, respectively, as in the case of large perturbations. When the perturbations are small and R0>1R0>1, we construct a new class of stochastic Lyapunov functions to show the ergodic property and the positive recurrence, and our results reveal some cycling phenomena of recurrent diseases. Computer simulations are carried out to illustrate our analytical results.
ORCID iDs
Yang, Qingshan and Mao, Xuerong ORCID: https://orcid.org/0000-0002-6768-9864;-
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Item type: Article ID code: 46676 Dates: DateEventJune 2013PublishedNotes: I have now added a copy of Professor Mao's paper Subjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 13 Feb 2014 17:10 Last modified: 20 Sep 2024 00:32 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/46676