Non-local compartment models, delay differential equations, and an interesting function

Abstract

Compartment models have a long history of use in mathematical modelling, underpinning many areas of practice including epidemiology, pharmacokinetics, and mathematical biology. These models consider the flow of objects (or people or energy) between different states that are referred to as compartments. There is continued interest in the generalisation of compartment models with the inclusion of non-local operators such as fractional order derivatives.  I will present a method of constructing compartment models with non-local operators that avoids many of the common pitfalls. This construction is achieved by first considering a non-Markovian stochastic process consisting of particles that are jumping between compartments. The non-local equations arise upon consideration of the mean of the process. Examples will be given of fractional order models as well as some simple delay differential equations. I will also highlight an interesting, but simple, function that arose in this work and talk about its relationship with both the solution of delay differential equation and a probability distribution. This talk is largely based on our recent SIAM Review SIGEST paper.
 
Zoom link: https://uni-sydney.zoom.us/j/81269414119?pwd=Z1FJTlZlUElMSHJTWDRPWjJOcG5...
Passcode: 973769

School Seminar Series: 

• Applied Seminar