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

Benkirane, Soufiene; Norman, Rachel; Scott, Erin; Shankland, Carron

doi:10.1007/978-3-642-32759-9_11

Cited by 7 publications

(7 citation statements)

References 19 publications

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“…The model is parameterised and validated on data up to 2015, and then to further validate its predictive performance it is shown to match 2016 data provided by HPS. The advantages for using the Bio-PEPA formalism (a mathematically-defined computational modeling approach called process algebra) have been fully argued in many works (Ciocchetta and Hillston, 2009 ; Benkirane et al, 2012 ; Hamami and Atmani, 2013 ). Here, the advantages are: formal structuring of interactions between components, a compositional approach to building the epidemiological model, and a range of analysis techniques to support the modeler in understanding the system.…”

Section: Mumps Epidemiology In Scotlandmentioning

confidence: 99%

Waning Immunity Is Associated with Periodic Large Outbreaks of Mumps: A Mathematical Modeling Study of Scottish Data

et al. 2017

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Vaccination programs for childhood diseases, such as measles, mumps and rubella have greatly contributed to decreasing the incidence and impact of those diseases. Nonetheless, despite long vaccination programmes across the world, mumps has not yet been eradicated in those countries: indeed, large outbreaks continue. For example, in Scotland large outbreaks occurred in 2004, 2005, and 2015, despite introducing the MMR (Measles-Mumps-Rubella) vaccine more than 20 years ago. There are indications that this vaccine-preventable disease is re-emerging in highly vaccinated populations. Here we investigate whether the resurgence of mumps is due to waning immunity, and further, could a booster dose be the solution to eradicate mumps or would it just extend the period of waning immunity? Using mathematical modeling we enhance a seasonally-structured disease model with four scenarios: no vaccination, vaccinated individuals protected for life, vaccinated individuals at risk of waning immunity, and introduction of measures to increase immunity (a third dose, or a better vaccine). The model is parameterised from observed clinical data in Scotland 2004–2015 and the literature. The results of the four scenarios are compared with observed clinical data 2004–2016. While the force of infection is relatively sensitive to the duration of immunity and the number of boosters undertaken, we conclude that periodic large outbreaks of mumps will be sustained for all except the second scenario. This suggests that the current protocol of two vaccinations is optimal in the sense that while there are periodic large outbreaks, the severity of cases in vaccinated individuals is less than in unvaccinated individuals, and the size of the outbreaks does not decrease sufficiently with a third booster to make economic sense. This recommendation relies on continuous efforts to maintain high levels of vaccination uptake.

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Section: Mumps Epidemiology In Scotlandmentioning

confidence: 99%

Waning Immunity Is Associated with Periodic Large Outbreaks of Mumps: A Mathematical Modeling Study of Scottish Data

et al. 2017

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“…Bio-PEPA has been adopted to analyse a number of biological systems (Ciocchetta and Hillston 2012) and disease spread (Benkirane et al 2012), but it has also been used to analyse emergency egress (Massink et al 2012c) and crowd dynamics (Massink et al 2011b) which are systems characterised by a high number of individuals and lack of a centralised controller, aspects common also to swarm robotics systems. Bio-PEPA is well suited to analyse and develop swarm robotics systems; with Bio-PEPA it is possible to develop a specification at the microscopic level while providing also primitives for spatial description (e.g.…”

Section: Introductionmentioning

confidence: 99%

On the use of Bio-PEPA for modelling and analysing collective behaviours in swarm robotics

et al. 2013

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In this paper we analyse a swarm robotics system using Bio-PEPA. Bio-PEPA is a process algebra language originally developed to analyse biochemical systems. A swarm robotics system can be analysed at two levels: the macroscopic level, to study the collective behaviour of the system, and the microscopic level, to study the robot-to-robot and robot-toenvironment interactions. In general, multiple models are necessary to analyse a system at different levels. However, developing multiple models increases the effort needed to analyse a system and raises issues about the consistency of the results. Bio-PEPA, instead, allows the researcher to perform stochastic simulation, fluid flow (ODE) analysis and statistical model checking using a single description, reducing the effort necessary to perform the analysis and ensuring consistency between the results. Bio-PEPA is well suited for swarm robotics systems: by using Bio-PEPA it is possible to model distributed systems and their spacetime characteristics in a natural way. We validate our approach by modelling a collective decision-making behaviour.

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“…PEPA has been used in system biology to model the raf kinase inhibitor protein on the extracellular signal regulated kinase signalling pathway [19] and to model measles epidemics in the UK from 1944-1964 [11].…”

Section: Stochastic Process Calculimentioning

confidence: 99%

A general overview of formal languages for individual-based modelling of ecosystems

Toro

2019

Journal of Logical and Algebraic Methods in Programming

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Various formal languages have been proposed in the literature for the individualbased modelling of ecological systems. These languages differ in their treatment of time and space. Each modelling language offers a distinct view and techniques for analyzing systems. Most of the languages are based on process calculi or P systems. In this article, we present a general overview of the existing modelling languages based on process calculi. We also discuss, briefly, other approaches such as P systems, cellular automata and Petri nets. Finally, we show advantages and disadvantages of these modelling languages and we propose some future research directions.

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

Cited by 7 publications

References 19 publications

Waning Immunity Is Associated with Periodic Large Outbreaks of Mumps: A Mathematical Modeling Study of Scottish Data

Waning Immunity Is Associated with Periodic Large Outbreaks of Mumps: A Mathematical Modeling Study of Scottish Data

On the use of Bio-PEPA for modelling and analysing collective behaviours in swarm robotics

A general overview of formal languages for individual-based modelling of ecosystems

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