On a stochastic epidemic SEIHR model and its diffusion approximation

• Marco Ferrante ^[1] ; Elisabetta Ferraris ^[1] ; Carles Rovira ^[2]
  1. [1] University of Padua

     University of Padua

     Padova, Italia

     
  2. [2] Universitat de Barcelona

     Universitat de Barcelona

     Barcelona, España

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 25, Nº. 3, 2016, págs. 482-502
• Idioma: inglés
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• Resumen

  • 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 R0 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.