Biometrika · 1955 · 257 citations · 4 references
Veterinary MedicineInfectious DiseasesEpidemiologyProbability TheoryStochastic ProcessesDisease SpreadInfectious Disease DynamicsMarkov ProcessesTransmission DynamicsEpidemic ContagionEpidemic ModelsEpidemic Population DynamicsEpidemic Spreading ModelsEpidemic Threshold AnalysisMathematical Modeling Of EpidemicsModeling Of Outbreak SpreadStochastic Epidemic Models
Bailey (1953) extended Bartlett’s stochastic epidemic model, showing that the distribution of the final epidemic size can be obtained by solving doubly recurrent relations. The author aims to demonstrate that, in general, these probabilities can be derived via singly recurrent relations. This is achieved by solving the singly recurrent relations (eqs. 17 and 24) and deriving expressions (eqs. 38 and 40) for the take‑off probability, providing a stochastic analogue of the Kermack–McKendrick threshold.
In a recent paper (1953) N. Bailey has considered a stochastic epidemic model of the type set up by Bartlett (1949), and has shown that the probability distribution (Pw) of the ultimate number of infected individuals (w) may be calculated by solving a certain set of doubly recurrent relations. I propose to show that for quite a general case these same probabilities may be obtained by the solution of a set of singly recurrent relations (eqs. (17) and (24)). Furthermore, an expression may be derived (eqs. (38) and (40)) for the probability that an infection introduced into a large population will 'take'—this provides a stochastic equivalent to Kermack & McKendrick's threshold theorem (1927 and later).
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THE TOTAL SIZE OF A GENERAL STOCHASTIC EPIDEMIC
Norman T. J. Bailey · Biometrika · 1953 · 111 citations