Biomaterial Database

Reproduction numbers and thresholds in stochastic epidemic models. I. Homogeneous populations. 1991

J A Jacquez, and P O'Neill

Department of Physiology, University of Michigan, Ann Arbor.

We compare threshold results for the deterministic and stochastic versions of the homogeneous SI model with recruitment, death due to the disease, a background death rate, and transmission rate beta cXY/N. If an infective is introduced into a population of susceptibles, the basic reproduction number, R0, plays a fundamental role for both, though the threshold results differ somewhat. For the deterministic model, no epidemic can occur if R0 less than or equal to 1 and an epidemic occurs if R0 greater than 1. For the stochastic model we find that on average, no epidemic will occur if R0 less than or equal to 1. If R0 greater than 1, there is a finite probability, but less than 1, that an epidemic will develop and eventuate in an endemic quasi-equilibrium. However, there is also a finite probability of extinction of the infection, and the probability of extinction decreases as R0 increases above 1.

UI	MeSH Term	Description	Entries
D007239	Infections	Invasion of the host organism by microorganisms or their toxins or by parasites that can cause pathological conditions or diseases.	Infection,Infection and Infestation,Infections and Infestations,Infestation and Infection,Infestations and Infections
D008954	Models, Biological	Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.	Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D003198	Computer Simulation	Computer-based representation of physical systems and phenomena such as chemical processes.	Computational Modeling,Computational Modelling,Computer Models,In silico Modeling,In silico Models,In silico Simulation,Models, Computer,Computerized Models,Computer Model,Computer Simulations,Computerized Model,In silico Model,Model, Computer,Model, Computerized,Model, In silico,Modeling, Computational,Modeling, In silico,Modelling, Computational,Simulation, Computer,Simulation, In silico,Simulations, Computer
D004196	Disease Outbreaks	Sudden increase in the incidence of a disease. The concept includes EPIDEMICS and PANDEMICS.	Outbreaks,Infectious Disease Outbreaks,Disease Outbreak,Disease Outbreak, Infectious,Disease Outbreaks, Infectious,Infectious Disease Outbreak,Outbreak, Disease,Outbreak, Infectious Disease,Outbreaks, Disease,Outbreaks, Infectious Disease
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