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Matrix-geometric methods for the general stochastic epidemic. 1984

J Gani, and P Purdue

Department of Statistics, University of Kentucky.

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.

UI	MeSH Term	Description	Entries
D008962	Models, Theoretical	Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment.	Experimental Model,Experimental Models,Mathematical Model,Model, Experimental,Models (Theoretical),Models, Experimental,Models, Theoretic,Theoretical Study,Mathematical Models,Model (Theoretical),Model, Mathematical,Model, Theoretical,Models, Mathematical,Studies, Theoretical,Study, Theoretical,Theoretical Model,Theoretical Models,Theoretical Studies
D004813	Epidemiology	Field concerned with the determination of causes, incidence, and characteristic behavior of disease outbreaks affecting human populations. It includes the interrelationships of host, agent, and environment as related to the distribution and control of disease.	Social Epidemiology,Epidemiologies, Social,Epidemiology, Social,Social Epidemiologies
D006801	Humans	Members of the species Homo sapiens.	Homo sapiens,Man (Taxonomy),Human,Man, Modern,Modern Man
D013269	Stochastic Processes	Processes that incorporate some element of randomness, used particularly to refer to a time series of random variables.	Process, Stochastic,Stochastic Process,Processes, Stochastic