A discrete-time model with vaccination for a measles epidemic

L. J.S. Allen, M. A. Jones, C. F. Martin

Research output: Contribution to journalArticle

21 Scopus citations

Abstract

A discrete-time, age-independent SIR-type epidemic model is formulated and analyzed. The effects of vaccination are also included in the model. Three mathematically important properties are verified for the model: solutions are nonnegative, the population size is time-invariant, and the epidemic concludes with all individuals either remaining susceptible or becoming immune (a property typical of SIR models). The model is applied to a measles epidemic on a university campus. The simulated results are in good agreement with the actual data if it is assumed that the population mixes nonhomogeneously. The results of the simulations indicate that a rate of immunity greater than 98% may be required to prevent an epidemic in a university population. The model has applications to other contagious diseases of SIR type. Furthermore, the simulated results of the model can easily be compared to data, and the effects of a vaccination program can be examined.

Original languageEnglish
Pages (from-to)111-131
Number of pages21
JournalMathematical Biosciences
Volume105
Issue number1
DOIs
StatePublished - Jun 1991

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