2007 Student Research Conference:

20th Annual Student Research Conference

20th Annual Student Research Conference

**Mathematical Properties of a Gamma-Function Distributed Epidemic Model**

Ross A. Coleman

Dr. Kenneth Carter, Faculty Mentor

Differential equation compartment models are often used to describe the spread of disease. Commonly used models implicitly assume that the probability an individual remains infectious for a given time is exponentially distributed. This assumption significantly overestimates the standard deviation for the time that individuals remain infectious. However, splitting the infectious class into a consecutive series of infectious classes decreases the standard deviation. The presentation will show that consecutive infectious compartments create a distribution for the time that individuals remain infectious which is a ratio between an incomplete and complete gamma function. While increasing the number of classes decreases the standard deviation, it does not change the basic reproduction number (the average number of individuals infected by a single infectious individual in a completely susceptible population). Gamma distributed models appear to predict the effectiveness of social distancing measures, such as quarantine, more accurately than the ubiquitous exponentially-distributed models do.

**Keywords:** epidemiology, compartment models, gamma function, applied math, population dynamics

**Topic(s):**Mathematical Biology

**Presentation Type:** Oral Paper

**Session:** 39-1

**Location:** VH 1432

**Time:** 1:30 pm