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On a stochastic epidemic SEIHR model and its diffusion approximation

Author

Listed:
  • Marco Ferrante

    (Università degli Studi di Padova)

  • Elisabetta Ferraris

    (Università degli Studi di Padova)

  • Carles Rovira

    (Facultat de Matemàtiques, Universitat de Barcelona)

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.

Suggested Citation

  • Marco Ferrante & Elisabetta Ferraris & Carles Rovira, 2016. "On a stochastic epidemic SEIHR model and its diffusion approximation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 482-502, September.
    • Handle: RePEc:spr:testjl:v:25:y:2016:i:3:d:10.1007_s11749-015-0465-z
    DOI: 10.1007/s11749-015-0465-z
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    References listed on IDEAS

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    1. Küchler, Uwe & Platen, Eckhard, 2000. "Strong discrete time approximation of stochastic differential equations with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 189-205.
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