TRANSITION PROBABILITIES FOR GENERALIZED SIR EPIDEMIC MODEL
Journal article, 2012
Gani and Purdue outlined a matrix-geometric method for determining the total size distribution of an epidemic in a recursive manner. In this article, we explore how this method can be used to study an SIR epidemic model with a generalized mechanism of infection. We are able to obtain an explicit formula for the Laplace transform of the transition probabilities. Using this we derive various other quantities explicitly. Examples of such quantities are the transition probabilities and the expectation of the duration of the epidemic.
infection
SIR model
Transition probabilities
spread
removal rate-functions
stochastic epidemic
Duration of an epidemic
Generalized infection mechanism
Matrix-geometric
Author
H. El Maroufy
Universite Sultan Moulay Slimane de Beni-Mellal
L. Omari
Universite Sidi Mohamed Ben Abdellah
Ziad Taib
University of Gothenburg
Chalmers, Mathematical Sciences, Mathematical Statistics
Stochastic Models
1532-6349 (ISSN) 1532-4214 (eISSN)
Vol. 28 1 15-28Subject Categories
Probability Theory and Statistics
DOI
10.1080/15326349.2011.614201