ICMS »

Networks: stochastic models for populations and epidemics

Sep 12, 2011 - Sep 16, 2011

ICMS, 15 South College Street

Organisers

Name	Institution
Britton, Tom	Stockholm University
Luczak, Malwina	Queen Mary University London
Neal, Peter	University of Manchester

The area of epidemic and population modelling is topical and abundant in intense research activity. The organisers of this workshop bring together researchers actively involved in the areas of networks and probabilistic models of epidemics and populations. The workshop will present an opportunity for the exchange of ideas and new collaborations amongst researchers promoting further developments in the field.

Photo of delegates

Workshop delegates - Wednesday 14 September [download the high resolution version for printing here]

Denis Mollison has created a website for the workshop, with most slides available through the "talks" section.

Arrangements

Participation
Participation is by invitation only. Invitees will be contacted by email.

UK Visas
If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and if so how to apply for one.

Venue
The workshop will be held at 15 South College Street, Edinburgh. You may find this map useful for the workshop. All lectures will be held in the Newhaven Lecture Theatre. In addition, two blackboards have recently been installed. The projector and one board may be used simultaneously.

Wireless Access
The workshop venue, 15 South College Street, has wireless access throughout. On arrival at Registration you will be given instructions and a code for accessing the wireless network. For those without laptops, there will also be a couple of computers available for you to check your emails.

Travel
The workshop will commence on Monday 12 September in the morning and will close at lunchtime on Friday 16 September to enable participants to travel that day. Please take these timings into account when organising your travel.

Information about travel to the UK and Edinburgh is available here.

Please note that it is your responsibility to have adequate travel insurance to cover medical and other emergencies that may occur on your trip.

A taxi directly from the airport will cost approximately 15.00 to 20.00 GBP to the city centre for a one-way journey. There is also a bus service direct from the airport to the city centre which will cost 3.50 single or 6.00 GBP return - the Airlink 100. This is a frequent service (every 10 minutes during peak times) and will bring you close to Waverley Railway Station, only a short walk to the accommodation and the workshop venue.

Lothian buses charge £1.30 for a single, £3.20 for a day ticket. Please note that the exact fare is required and no change is given.

If travelling by train, please note that Edinburgh has two railway stations - Waverley Railway Station being the main station and closest to the workshop venue at 15 South College Street. If you alight at Edinburgh Waverley, the workshop venue is an easy 10 minute walk over North and South Bridge. The second railway station is called Haymarket and is at the West End of the city centre.

Programme

Programme published 2 September 2011. Programme may be adjusted without prior notification.

Monday 12 September

08.30 - 09.00	Registration
09.00 - 10.00	Denis Mollison (Heriot-Watt University) Network models for epidemics
10.00 - 10.30	Coffee and tea (served in the Chapterhouse)
10.30 - 11.30	Alexander Holroyd (Microsoft Research) Invariant matching
11.30 - 12.30	Maria Deijfen (Stockholm University) Scale-free percolation
12.30 - 14.00	Lunch served in the Chapterhouse
14.00 - 15.00	Mathew Penrose (Univeristy of Bath) Random geometric graphs
15.00 - 16.00	Valerie Isham (University College London) Spread of information/infection on networks
16.00 - 16.30	Coffee and tea
16.30 - 17.30	Frank Ball (University of Nottingham) Epidemics on random networks with household structure

Tuesday 13 September

09.00 - 09.45	Vlada Limic (Université de Provence) Exchangable coalescents
09.45 - 10.30	Etienne Pardoux (Université de Provence) Continuous limit of probabilistic models of population with interaction
10.30 - 11.00	Coffee and tea served in the Chapterhouse
11.00 - 12.30	Group session/Open problems
12.00 - 14.00	Lunch break
14.00 - 15.30	Group session/Open problems
15.30 - 16.00	Coffee and tea served in the Chapterhouse
16.00 - 16.45	Remco van der Hofstad (TU Eindhoven) Hypercube percolation
16.45- 17.30	Peter Neal (University of Manchester) Variance of the giant component of a random graph

Wednesday 14 September

09.00 - 09.45	Lorenzo Pellis (Imperial College London) R_0 and other reproduction numbers for epidemic models with household structure
09.45 - 10.30	Pieter Trapman (Stockholm University) SIR epidemics on random intersection graphs
10.30 - 11.00	Coffee and tea served in the Chapterhouse
11.00 - 12.30	Group session/Open problems
12.00 - 14.00	Lunch break
	Knowledge Transfer Session
14.00 - 14.30	Tommi Asikainen (ECDC) Presentation of ECDC, modelling networks and data availability
14.30 - 15.00	Piero Poletti (ECDC) ECDC work on varicella vaccination modelling in EU/EEA/EFTA countries
15.00 - 15.30	Gianpaolo Scalia-Tomba (ECDC) ECDC work on generation times in epidemic modelling
15.30 - 16.00	Coffee and tea served in the Chapterhouse
16.00 - 16.30	Ard van Sighem (ECDC) ECDC work on estimating HIV prevalence in EU/EEA/EFTA countries
16.30 - 17.00	Ian Hall (HPA) Building behavioural response effects into stochastic models for contingency planning
17.00 - 17.30	Iain Barrass (HPA) Interpretation of large-scale stochastic epidemic models
17.30 - 18.30	Wine reception

Thursday 15 September

09.00 - 09.45	Damian Clancy (University of Liverpool) The effects of population heterogeneities on spread of infection
09.45 - 10.30	Mirjam Kretzschmar (University Medical Centre Utrecht ) Dynamic pair formulation models
10.30 - 11.00	Coffee and tea served in the Chapterhouse
11.00 - 12.30	Group session/Open problems
12.30 - 14.00	Lunch break
14.00 - 15.30	Group session/Open problems
15.30 - 16.00	Coffee and tea served in the Chapterhouse
16.00 - 16.45	Theo Kypraios & Philip O'Neill (University of Nottingham) Statistical inference for epidemics on networks
16.45 - 17.30	Boris Schmid (Utrecht University) How does the sexual behaviour of individuals relate to commonly used sexual behaviour summary measures
19.00	Workshop dinner

Friday 16 September

09.00 - 09.45	Joel Miller (Harvard School of Public Health) Edge-based compartmental models for epidemics on networks
09.45 - 10.30	Viet Chi Tran (Université Lille) Large graph limit and Volz' equations for an SIR epidemic spreading on a configuration model graph
10.30 - 11.00	Coffee and tea served in the Chapterhouse
11.00 - 12.30	Group session/Open problems
	End of workshop. Building open until 17.00

Presentations:

Presentation Details
Ball, Frank
Epidemics on random networks with household structure
View Abstract Hide Abstract
There has been a growing interest in models for epidemics among structured populations, which incorporate realistic departures from homogeneous mixing whilst maintaining mathematical tractability. Two classes of structured population epidemic models that have attracted considerable recent attention are network models (in which there is a random graph describing possible infectious contacts) and household models (in which the population is partitioned into households with different contact rates for within- and between-household infection). In this talk a model for the spread of an SIR (susceptible-infective-removed) epidemic that includes both of these features is described and analysed. The analysis includes deriving a threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak, and determining the probability and expected relative final size of a major outbreak. Extensions of the model, including some unsolved problems, are briefly discussed. Frank Ball (University of Nottingham), David Sirl (Loughborough University), Pieter Trapman (Stockholm University).
Barrass, Iain
Interpretation of large-scale stochastic epidemic models
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Modern computational systems have allowed the development of highly detailed models of disease dynamics. Stochastic agent-based and metapopulation models usually give rise to an ensemble of results which must be interpreted in some way. Within the large ensembles that can routinely be obtained quite varied behaviour can be observed. For a confident statement of results one must consider the predictive power of the models as well as how best to understand and present the variability seen. This talk presents recent work within HPA examining the issues around model selection, and predictability and interpretation of a contingency planning model in use. We examine how considerations of the model and its output depend on a study’s aims and how results can be visualised and then presented in a manner appropriate to the target audience.
Clancy, Damian
The effects of population heterogeneities on spread of infection
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Heterogeneities in individual infectivities, individual susceptibilities, and population mixing (assortative or dissortative) may all have effects upon infectious spread, compared to a corresponding homogeneous model. Specifically, the corresponding homogeneous model here is chosen to have the same value of the basic reproduction number R_0 as the heterogeneous model of interest. Effects of heterogeneity are considered in terms of (i) the probability of a major outbreak; (ii) the equilibrium prevalence level, given that infection becomes established; and (iii) the distribution of time until eventual fade-out of infection.
Deijfen, Maria
Scale-free percolation
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I will describe a model for inhomogeneous long-range percolation on Z^d with potential applications in network modelling. Each vertex is independently assigned a non-negative random weight and the probability that there is an edge between two given vertices is then determined by a certain function of their weights and of the distance between them. The results concern the degree distribution in the resulting graph, the percolation properties of the graph and the graph distance between remote pairs of vertices. The model interpolates between long-range percolation and inhomogeneous random graphs, and is shown to inherit the interesting features of both these model classes.
Hall, Ian
Building behavioural response effects into stochastic models for contingency planning
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Potential bioterrorist activity demands careful contingency planning to mitigate the likely impacts of a release and present communication challenges about uncertainty. The Health Protection Agency has been working on developing plans assuming releases of a number of possible agents (smallpox, plague and anthrax). However, often these models are left making assumptions about the public perceptions and responses to public health interventions. To provide a more evidence based approach to this problem we have performed population surveys to assess these factors for pneumonic plague and recently for pandemic influenza. Here we discuss the results of the surveys, the incorporation into a range of stochastic models (individual based and meta-population) and lessons learnt.
Kretzschmar, Mirjam
Dynamic pair formulation models
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I would like to discuss how to extend dynamic pair formation models to include some features of networks, for example describing models with dynamics stars instead of only dyads. This is a deterministic approach, but could of course also be formulated in a stochastic framework.
Kypraios, Theo
Statistical inference for epidemics on networks (joint talk with Philip O'Neill)
View Abstract Hide Abstract
We review different approaches to the problem of inferring model parameters for stochastic epidemic models defined on networks and highlight possible future research directions.
Miller, Joel
Edge-based compartmental models for epidemics on networks
View Abstract Hide Abstract
The potentially infectious contacts in a population can be represented by a network which controls how an infectious disease spreads. A number of results have been found for the final size of epidemics in random static networks with given degree distributions. However, relatively little has been known about their dynamics or what impact the changing structure of a contact network has on disease spread. We have recently developed an "edge-based compartmental modelling" approach that focuses on the status of edges rather than individuals. This approach allows us to calculate the dynamics of an epidemic spreading on a network in a straightforward way. The approach allows us to consider the impact of changes in the network structure as well as heterogeneity in contact levels among individuals. The resulting equations are comparable in complexity to the usual mass action SIR equations. I will demonstrate the approach with a simple network structure, and then discuss what features are needed for the approach to work more generally.
Mollison, Denis
Network models for epidemics
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A review of the history of network models for epidemics, discussing their relation to other models, and their advantages and disadvantages. At best, the network approach extends the situations and features that we can model, and facilitates new insights into epidemic dynamics and new data analysis techniques. But, as with all stochastic mathematics, sometimes we can be diverted into what is easy or mathematically attractive to model, into what is elegant rather than practically appropriate.
O'Neill, Philip
Statistical inference for epidemics on networks (joint with Theo Kypraios)
View Abstract Hide Abstract
We review different approaches to the problem of inferring model parameters for stochastic epidemic models defined on networks and highlight possible future research directions.
Pellis, Lorenzo
$R_0$ and other reproduction numbers for epidemic models with household structure.
View Abstract Hide Abstract
The basic reproduction number $R_0$ is one of the most important quantities in epidemiology. However, for epidemic models with explicit social structure involving small mixing units such as households, its definition is not straightforward and a wealth of other surrogate threshold parameters has appeared in the literature. I will show how to use branching processes to define $R_0$, apply this definition to models with households (or other more complex social structures) and provide methods for calculating it. Extending previous work, I will provide a complete overview of the inequalities holding among existing threshold parameters, including $R_0$. I will show how random vaccination of a fraction $1-1/R_0$ of the population is not enough to prevent large epidemics and I will provide sharper bounds than the existing ones for bracketing the critical vaccination coverage associated with a perfect vaccine between analytically tractable quantities.
Scalia-Tomba, Gianpaolo
ECDC work on generation times in epidemic modelling
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There has been recent interest in the so called generation time in epidemic models, i.e. the average time between the infection of a primary case and one of its secondary cases. It is related to the latent and infectious period distributions and is involved in a useful relationship between initial speed of growth and the basic reproductive number R0 in SIR models. The natural framework for considerations about various times in epidemic models and analysis of their statistical properties is stochastic. Various facts about the generation time distribution will be presented and links to demography and statistics will also be discussed. References SCALIA TOMBA G., SVENSSON Å., ASIKAINEN T. and GIESECKE J. (2010): Some model based considerations on observing generation times for communicable diseases. Mathematical Biosciences, 223, 24-31.
Schmid, Boris
How does the sexual behaviour of individuals relate to commonly used sexual behaviour summary measures.
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(Boris V Schmid and Mirjam Kretzschmar) There are four major quantities that are measured in sexual behaviour surveys that are thought to be especially relevant for the performance of sexual network models in terms of disease transmission. These are (i) the cumulative distribution of lifetime number of partners, (ii) the distribution of partnership durations, (iii) the distribution of gap lengths between partnerships, and (iv) the number of recent partners. Fitting a network model to these quantities as measured in sexual behaviour surveys is expected to result in a good description of Chlamydia trachomatis (Ct) transmission in terms of the heterogeneity of the distribution of infection in the population. Here we present work on how these population level summary measures depend on four sexual behaviours and their heterogeneity on the individual level; namely the onset of sexual availability, partner age preference, partnership type preference, and the ability to maintain concurrent partnerships. We use an individual based simulation model that defines individuals in terms of their personal sexual behaviour, and demonstrate how including sexual behaviour on the individual level improved the performance of the model in describing population level measures of sexual behaviour, compared to the original Kretzschmar model from 1996.
Tran, Viet Chi
Large graph limit and Volz' equations for an SIR epidemic spreading on a configuration model graph
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We consider an SIR epidemic model propagating on a Configuration Model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles. These three degree distributions are sufficient to describe the course of the disease. The limit in large population is investigated. This allows us to provide a rigorous proof of the equations obtained by Volz (2008) where the spread of the epidemics is summed up into 5 ordinary differential equations only.
Trapman, Pieter
SIR epidemics on random intersection graphs
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We consider a model for the spread of a stochastic SIR epidemic on a network of individuals described by a random intersection graph. The number of cliques a typical individual belongs to follows a mixed-Poisson distribution, as does the size of a typical clique. Infection can be transmitted between two individuals if and only if they belong to the same clique. An infinite-type branching process approximation (with type being given by the length of an individual's infectious period) for the early stages of an epidemic is developed and made fully rigorous by proving an associated limit theorem as the population size tends to infinity. This leads to a threshold parameter R*. We also provide a law of large numbers for the size of such a large outbreak. This talk is based on joint work with Frank Ball and David Sirl.
van der Hofstad, Remco
Hypercube percolation
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Consider bond percolation on the hypercube {0,1}^n at the critical probability p_c defined such that the expected cluster size equals 2^{n/3}, where 2^{n/3} acts as the cube root of the number of vertices of the n-cube. Percolation on the Hamming cube was proposed by Erd"os and Spencer (1979), and has proved to be substantially harder than percolation on the complete graph. In this talk, I will describe the phase transition for percolation on the hypercube, and show that it shares many features with that on the complete graph. In previous work, we have identified the subcritical and critical regimes of percolation on the hypercube. In particular, we know that for p=p_c(1+O(2^{-n/3})), the largest connected component is of size roughly 2^{2n/3} and that this quantity is non-concentrated. So far, we were missing an analysis of the behavior of the largest connected component above the critical value, to show that the critical value really is critical. In this work, we identify the supercritical behavior of percolation on the hypercube, by showing that, for any sequence epsilon_n tending to zero, but epsilon_n being much larger than 2^{-n/3}, percolation at p_c(1+epsilon_n) has, with high probability, a unique giant component of size (2+o(1))epsilon_n 2^n. (This is joint work with Asaf Nachmias, building on previous work with Markus Heydenreich, Gordon Slade, Christian Borgs, Jennifer Chayes and Joel Spencer).

Participants

Name	Institution
Asikainen, Tommi	European Centre for Disease Prevention and Control
Ball, Frank	University of Nottingham
Barrass, Iain	Health Protection Agency
Brightwell, Graham	London School of Economics
Britton, Tom	Stockholm University
Cannings, Chris	University of Sheffield
Clancy, Damian	University of Liverpool
Deijfen, Maria	Stockholm University
Ford, Ashley	University of Warwick
Gamado, Kokouvi Mawuli	BioSS and Heriot-Watt University
Hall, Ian	Health Protection Agency
Holroyd, Alexander	Microsoft Research
Isham, Valerie	University College London
Janson, Svante	Uppsala University
Jordan, Jonathan	University of Sheffield
Kretzschmar, Mirjam	University Medical Centre Utrecht
Kypraios, Theo	University of Nottingham
Limic, Vlada	Université de Provence
Lopes, Fabio	Stockholm University
Luczak, Malwina	Queen Mary University London
Miller, Joel	Harvard School of Public Health
Mollison, Denis	Heriot-Watt University
Neal, Peter	University of Manchester
O'Neill, Philip	University of Nottingham
Pardoux, Etienne	Université de Provence
Pellis, Lorenzo	Imperial College London
Penrose, Mathew	University of Bath
Poletti, Piero	Bruno Kessler Foundation
Reinert, Gesine	University of Oxford
Rippl, Thomas	University Goettingen
Scalia-Tomba, Gianpaolo	University of Rome Tor Vergata
Schmid, Boris	RIVM, National Institute for Public Health and the Environment
Tran, Viet Chi	Université Lille 1
Trapman, Pieter	Stockholm University
Turner, Amanda	Lancaster University
van der Hofstad, Remco	Eindhoven University of Technology
van Sighem, Ard	University of Amsterdam