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On the time to reach a critical number of infections in epidemic models with infective and susceptible immigrants.

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Almaraz Luengo, Elena and Gómez-Corral, Antonio and Rodríguez Bernal, María Teresa (2016) On the time to reach a critical number of infections in epidemic models with infective and susceptible immigrants. BioSystems, 144 (1). pp. 68-77. ISSN 03032647

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Official URL: http://www.sciencedirect.com/science/article/pii/S030326471630048X


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Abstract

In this paper we examine the time T to reach a critical number K0 of infections during an outbreak in an epidemic model with infective and susceptible immigrants. The underlying process X, which was first introduced by Ridler-Rowe (1967), is related to recurrent diseases and it appears to be analytically intractable. We present an approximating model inspired from the use of extreme values, and we derive formulae for the Laplace-Stieltjes transform of T and its moments, which are evaluated by using an iterative procedure. Numerical examples are presented to illustrate the effects of the contact and removal rates on the expected values of T and the threshold K0, when the initial time instant corresponds to an invasion time. We also study the exact reproduction number Rexact,0 and the population transmission number Rp, which are random versions of the basic reproduction number R0.


Item Type:Article
Uncontrolled Keywords:Critical threshold; Immigration; Maximum number of infectives; Stochastic epidemic
Subjects:Sciences > Mathematics > Operations research
ID Code:38180
Deposited On:23 Jun 2016 08:23
Last Modified:21 Nov 2016 10:06

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