Term of Award

Spring 1998

Degree Name

Master of Science in Applied Mathematics

Document Type and Release Option

Thesis (restricted to Georgia Southern)

Committee Chair

John W. Davenport

Committee Member 1

Lila F. Roberts

Committee Member 2

Eric T. Funasaki

Abstract

The spread of some childhood diseases such as chickenpox, measles, mumps, and rubella can be modeled by a system of ordinary differential equations. The total population, assumed to be constant, is subdivided into four categories: susceptible, exposed, infected, and recovered. The coefficient of the interaction term between susceptible and infected individuals, the contact rate, measures the contagiousness of the disease. A system with a constant contact rate is considered but the results are inconsistent with available data. A system with a sinusoidal contact rate is considered which numerically yields both periodic and chaotic solutions. While this behavior mimics that of the available data, the seasonal forcing is too great. Finally we consider a system with a piecewise linear contact rate and compare its results to the sinusoidal system. Erratic fluctuations are achieved in the piecewise system at levels of seasonal forcing lower than required in the sinusoidal system.

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