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 language | English |
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Pages (from-to) | 111-131 |
Number of pages | 21 |
Journal | Mathematical Biosciences |
Volume | 105 |
Issue number | 1 |
DOIs | |
State | Published - Jun 1991 |