Matrix-geometric methods for the general stochastic epidemic.
This paper outlines a matrix-geometric formulation of the general stochastic epidemic for the case of a generalized infection mechanism. The forward Kolmogorov equations of the system are derived, and the Laplace transforms of the state probabilities obtained recursively. These lead to the probabilities of survivors of the epidemic. The stochastic threshold theorem for the generalized case is stated.
D004813:Epidemiology; D006801:Humans; D008962:Models, Theoretical; D013269:Stochastic Processes