On a stochastic epidemic SEIHR model and its diffusion approximation

Marco Ferrante (), Elisabetta Ferraris () and Carles Rovira ()
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Marco Ferrante: Università degli Studi di Padova
Elisabetta Ferraris: Università degli Studi di Padova
Carles Rovira: Facultat de Matemàtiques, Universitat de Barcelona

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2016, vol. 25, issue 3, No 5, 482-502

Abstract: Abstract To model the evolution of diseases with extended latency periods like varicella, we generalise a simple discrete time stochastic SIR-type epidemic model of Tuckwell and Williams. We include both latent periods as well as the presence of quarantine areas, to capture the evolutionary dynamics of such diseases. Analytical results of the proposed Markovian model are provided. The basic reproduction number $$R_0$$ R 0 of the former and new models as well as a diffusion approximation are derived, leading to a stochastic differential equation with multiple delays in a natural way.

Keywords: SIR model; SEIHR model; Basic reproduction number; Stochastic delay differential equations; 92D30; 60J10; 60H10 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11749-015-0465-z

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