Date of Award

8-2018

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

Committee Member

Dr. Xin Liu, Committee Chair

Committee Member

Dr. Peter Kiessler

Committee Member

Dr. Brian Fralix

Abstract

We study a stochastic SIS (Susceptible-Infected-Susceptible) epidemic model, in which individu-als in a population are divided into two classes: “Susceptible” to the infection of a disease, and “Infected” by the disease. We assume the population size N is fixed. The state process, which measures the num-ber of infected individuals, is modeled as a continuous time Markov chain (CTMC). The CTMC has an absorbing state 0, and it will eventually die out by reaching the absorbing state. However, it appears to be persistent over a long time period before extinction. Such behavior can be understood by the study of quasi-stationary distributions. In this thesis, our main results show that the CTMC SIS model has a unique quasi-stationary distribution, and when the basic reproduction number is greater than 1, as N → ∞, the quasi-stationary distribution converges to a dirac probability measure concentrated at the equilibrium point of a deterministic SIS model.

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