Final outcome probabilities for SIR epidemic model

Abstract

We consider an SIR stochastic epidemic model in which new infections occur at rate f(x, y), where x and y are, respectively, the number of susceptibles and infectives at the time of infection and f is a positive sequence of real functions. A simple explicit formula for the final size distribution is obtained. Some efficient recursive methods are proved for the exact calculation of this distribution. In addition, we give a Gaussian approximation for the final distribution using a diffusion process approximation.

Keywords:

• Stochastic epidemic model
• Markov chain
• Final size
• Diffusion process.

MATHEMATICS SUBJECT CLASSIFICATION:

• 92D30
• 60J28
• 68J20
• 65C20

Acknowledgments

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