TRANSITION PROBABILITIES FOR GENERALIZED SIR EPIDEMIC MODEL

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

Duration of an epidemic

Generalized infection mechanism

Matrix-geometric

Transition probabilities

SIR model

removal rate-functions

stochastic epidemic

infection

spread

infection

Publication and Content Type

ref (subject category)

art (subject category)