title: A discrete-time model with vaccination for a measles epidemic.
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.
authors.affiliation: Department of Mathematics, Texas Tech University, Lubbock 79409.
authors.forename: L J
authors.initials: LJ
authors.lastname: Allen
authors.forename: M A
authors.initials: MA
authors.lastname: Jones
authors.forename: C F
authors.initials: CF
authors.lastname: Martin
mesh_terms: D000293:Adolescent; D000328:Adult; D000367:Age Factors; D004196:Disease Outbreaks; D006801:Humans; D007114:Immunization; D008433:Mathematics; D008457:Measles / Q000453:epidemiology* / Q000517:prevention & control; D008458:Measles Vaccine / Q000008:administration & dosage; D015233:Models, Statistical; D013781:Texas / Q000453:epidemiology
chemical_list: D008458:Measles Vaccine