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A Markov Chain Model of Population Growth with an Application in Epidemiology
Author(s) -
Lefevre C.
Publication year - 1988
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710300207
Subject(s) - markov chain , mathematics , markov process , simple (philosophy) , markov model , population , variable order markov model , markov property , continuous time markov chain , bounded function , markov renewal process , discrete time and continuous time , econometrics , statistics , mathematical analysis , philosophy , demography , epistemology , sociology
This paper is concerned with a class of population growth processes in discrete time; the simple epidemic process is considered as a specific example. A Markov chain model is constructed and standard Markov methods are used to study the main biological concepts. A simple and explicit formula is obtained for the transient distribution of the population size. Then, the cost of the process is defined and the joint probability generating function of its components is derived. Finally, the results are extended to the case where the inter‐transition periods are bounded i.i.d. random variables.