Multi-Strain Influenza Models with Staged-Susceptibility

Mr. Thomas Park

Department of Mathematical Sciences
University of Alabama in Huntsville

October 29, 1999

Abstract

Modeling the spread of infectious diseases often involves partitioning the total population into classes based on the progress of the disease. For instance, if infection confers permanent immunity, the population may be divided into susceptible, infectious, and recovered classes. A system of differential equations modeling the flow between these compartments will be derived for this basic model (known as the S-I-R model). The reproductive number is the criteria which determines whether of not the disease will spread or die out. The reproductive number will be be derived for the S-I-R model and its significance will be discussed. Permanent immunity is not adequate to model influenza. We consider susceptibility as a series of stages through which an individual progresses after infection. The one-strain model for the staged-susceptibility case will be considered and the reproductive number will be derived. Inherently, the transmission of influenza is a multi-strain problem. Consequently, we link several staged-susceptibility models together to form a complete multi-strain model. Details of results to date will be discussed.