Research output

Article in Journal ()

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

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.

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.

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

AuthorsMcCaig Chris, Fenton Andrew, Graham Andrea, Shankland Carron, Norman Rachel
Publication date07/2013
Publication date online14/03/2013
Date accepted by journal04/03/2013
ISSN 0022-5193

Journal of Theoretical Biology: Volume 329

© University of Stirling FK9 4LA Scotland UK • Telephone +44 1786 473171 • Scottish Charity No SC011159
My Portal