A rigorous approach to investigating common assumptions about disease transmission

McCaig, Chris; Begon, Michael; Norman, Rachel; Shankland, Carron

doi:10.1007/s12064-010-0106-8

Cited by 7 publications

(2 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This extends previous studies and discussions of contact processes in epidemiology (see [5,16,37,57]) and provides a unifying mathematical validation for the notions of frequency-dependent versus density-dependent contact rates -both models can be recovered by taking different limits on the same underlying stochastic individual-level process. Whereas McCaig et al [36] took a cybernetic (algorithmic) approach to the same problem (i.e. scaling up from individual-level interactions to population-level transmission models), our approach provides an analytical treatment in which stochastic processes are modeled explicitely.…”

Section: Overview and Concluding Remarksmentioning

confidence: 99%

The effect of competition and horizontal trait inheritance on invasion, fixation, and polymorphism

Billiard

Collet

Ferrière

et al. 2016

Journal of Theoretical Biology

View full text Add to dashboard Cite

Horizontal transfer (HT) of heritable information or 'traits' (carried by genetic elements, endosymbionts, or culture) is widespread among living organisms. Yet current ecological and evolutionary theory addressing HT is limited. We present a modeling framework for the dynamics of two populations that compete for resources and exchange horizontally (transfer) an otherwise vertically inherited trait. Competition influences individual demographics, affecting population size, which feeds back on the dynamics of transfer. We capture this feedback with a stochastic individual-based model, from which we derive a deterministic approximation for large populations. The interaction between horizontal transfer and competition makes possible the stable (or bi-stable) polymorphic maintenance of deleterious traits (including costly plasmids). When transfer rates are of a general density-dependent form, transfer stochasticity contributes strongly to population fluctuations. For an initially rare trait, we describe the probabilistic dynamics of invasion and fixation. Acceleration of fixation by HT is faster when competition is weak in the resident population. Thus, HT can have a major impact on the distribution of mutational effects that are fixed, and our model provides a basis for a general theory of the influence of HT on eco-evolutionary dynamics and adaptation.

show abstract

Section: Overview and Concluding Remarksmentioning

confidence: 99%

The effect of competition and horizontal trait inheritance on invasion, fixation, and polymorphism

Billiard

Collet

Ferrière

et al. 2016

Journal of Theoretical Biology

View full text Add to dashboard Cite

show abstract

“…We will deal with each of these features, starting from the past work, showing important and missing aspects from the ecological point of view. The pioneers of using process algebras for ecological modelling were the group of Norman and Shankland in the Department of Computing Science and Mathematics of Stirling University with the project System Dynamics from Individual Interactions: A process algebra approach to epidemiology [17]. They were the first to underline the importance and usefulness of process algebra as a modelling methodology for epidemiology.…”

Section: Introductionmentioning

confidence: 99%

MELA: Modelling in Ecology with Location Attributes

Vissat¹,

Hillston²,

Marion³

et al. 2016

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

Ecology studies the interactions between individuals, species and the environment. The ability to predict the dynamics of ecological systems would support the design and monitoring of control strategies and would help to address pressing global environmental issues. It is also important to plan for efficient use of natural resources and maintenance of critical ecosystem services. The mathematical modelling of ecological systems often includes nontrivial specifications of processes that influence the birth, death, development and movement of individuals in the environment, that take into account both biotic and abiotic interactions. To assist in the specification of such models, we introduce MELA, a process algebra for Modelling in Ecology with Location Attributes. Process algebras allow the modeller to describe concurrent systems in a high-level language. A key feature of concurrent systems is that they are composed of agents that can progress simultaneously but also interacta good match to ecological systems. MELA aims to provide ecologists with a straightforward yet flexible tool for modelling ecological systems, with particular emphasis on the description of space and the environment. Here we present four example MELA models, illustrating the different spatial arrangements which can be accommodated and demonstrating the use of MELA in epidemiological and predator-prey scenarios.

show abstract

Measles Epidemics and PEPA: An Exploration of Historic Disease Dynamics Using Process Algebra

Benkirane

Norman

Scott

et al. 2012

FM 2012: Formal Methods

View full text Add to dashboard Cite

A rigorous approach to investigating common assumptions about disease transmission

Cited by 7 publications

References 41 publications

The effect of competition and horizontal trait inheritance on invasion, fixation, and polymorphism

The effect of competition and horizontal trait inheritance on invasion, fixation, and polymorphism

MELA: Modelling in Ecology with Location Attributes

Measles Epidemics and PEPA: An Exploration of Historic Disease Dynamics Using Process Algebra

Contact Info

Product

Resources

About