Transition Probabilities for Generalized SIR Epidemic Model

Abstract

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.

Keywords:

• Duration of an epidemic
• Generalized infection mechanism
• Matrix-geometric
• Transition probabilities
• SIR model

Mathematics Subject Classification:

• Primary 60J28
• Secondary 92D30

ACKNOWLEDGMENTS

The referees are kindly acknowledged for very interesting remarks and suggestions.

This article is part of the Special Issue in honor of Marcel F. Neuts, published in volume 27(4) of Stochastic Models.