Using process algebra to develop predator-prey models of within-host parasite dynamics

Citation

McCaig C, Fenton A, Graham A, Shankland C & Norman R (2013) Using process algebra to develop predator-prey models of within-host parasite dynamics. Journal of Theoretical Biology, 329, pp. 74-81. https://doi.org/10.1016/j.jtbi.2013.03.001

Abstract
As a first approximation of immune-mediated within-host parasite dynamics we can consider the immune response as a predator, with the parasite as its prey. In the ecological literature of predator-prey interactions there are a number of different functional responses used to describe how a predator reproduces in response to consuming prey. Until recently most of the models of the immune system that have taken a predator-prey approach have used simple mass action dynamics to capture the interaction between the immune response and the parasite. More recently Fenton and Perkins (2010) employed three of the most commonly used functional response terms from the ecological literature. In this paper we make use of a technique from computing science, process algebra, to develop mathematical models. The novelty of the process algebra approach is to allow stochastic models of the population (parasite and immune cells) to be developed from rules of individual cell behaviour. By using this approach in which individual cellular behaviour is captured we have derived a ratio-dependent response similar to that seen in previous models of immune-mediated parasite dynamics, confirming that, whilst this type of term is controversial in ecological predator-prey models, it is appropriate for models of the immune system.

Keywords
Immune system; Dynamics; Cellular interactions; WSCCS; Mathematical models; Ratiodependence

Journal
Journal of Theoretical Biology: Volume 329

People

Professor Rachel Norman

Chair in Food Security & Sustainability, Mathematics