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

Chris McCaig, A. Fenton, A. Graham, C. Shankland, R. Norman

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 prey-dependent 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 the 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.
LanguageEnglish
Pages74-81
Number of pages8
JournalJournal of Theoretical Biology
Volume329
DOIs
Publication statusPublished - 7 Jul 2013

Fingerprint

Process Algebra
Predator-prey Model
Prey
Algebra
Parasites
Predator-prey
Functional Response
Immune Response
Immune System
Predator
predators
parasites
Immune system
Ecological Model
Ratio-dependent
Cell
immune system
Term
Interaction
Stochastic Model

Keywords

  • process algebra
  • develop
  • predator-prey models
  • host parasite dynamics

Cite this

McCaig, Chris ; Fenton, A. ; Graham, A. ; Shankland, C. ; Norman, R. / Using process algebra to develop predator-prey models of within-host parasite dynamics. In: Journal of Theoretical Biology. 2013 ; Vol. 329. pp. 74-81.
@article{dd06b01c214e4558ad86a3323ff9af0f,
title = "Using process algebra to develop predator-prey models of within-host parasite dynamics",
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 prey-dependent 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 the 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 = "process algebra, develop, predator-prey models, host parasite dynamics",
author = "Chris McCaig and A. Fenton and A. Graham and C. Shankland and R. Norman",
year = "2013",
month = "7",
day = "7",
doi = "10.1016/j.jtbi.2013.03.001",
language = "English",
volume = "329",
pages = "74--81",
journal = "Journal of Theoretical Biology",
issn = "0022-5193",

}

Using process algebra to develop predator-prey models of within-host parasite dynamics. / McCaig, Chris; Fenton, A.; Graham, A.; Shankland, C.; Norman, R.

In: Journal of Theoretical Biology, Vol. 329, 07.07.2013, p. 74-81.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Using process algebra to develop predator-prey models of within-host parasite dynamics

AU - McCaig, Chris

AU - Fenton, A.

AU - Graham, A.

AU - Shankland, C.

AU - Norman, R.

PY - 2013/7/7

Y1 - 2013/7/7

N2 - 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 prey-dependent 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 the 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.

AB - 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 prey-dependent 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 the 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.

KW - process algebra

KW - develop

KW - predator-prey models

KW - host parasite dynamics

UR - http://www.scopus.com/inward/record.url?scp=84877085780&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1016/j.jtbi.2013.03.001

U2 - 10.1016/j.jtbi.2013.03.001

DO - 10.1016/j.jtbi.2013.03.001

M3 - Article

VL - 329

SP - 74

EP - 81

JO - Journal of Theoretical Biology

T2 - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

ER -