Marshall University Math Colloquium
February 22, 2012
Studying the recovery procedure for the time-dependent transmission rate in epidemic models.
In this talk I will discuss recent results on recovering the time-dependent transmission function for classical disease models given the disease incidence data. The recovery procedure is applied to a homogeneous population, meaning all individuals are equally likely to transmit the disease to any other individual. For a homogeneous epidemic model, there is one time-dependent transmission function. Also, the procedure is applied to a two population model, which has up to four distinct transmission functions. A two population model is appropriate for studying disease transmission in a heterogeneous population, for example, a population split into children and adults, who spread the disease differently among themselves. Determining the time-dependent transmission function that exactly reproduces disease incidence data can yield useful information about disease outbreaks, including a range potential values for the recovery rate of the disease and offers a method to test the "school year" hypothesis (seasonality) for disease transmission.
This will be a general audience talk. The talk will end with a discussion of several research projects that would be appropriate for a capstone project or a Master's thesis.