Workshop home page Participants Programme Photos Epidemics home page STNMD I, Rutgers 2003 STNMD II,Edinburgh 2007

Tubingen 21-25 October 2008

`Spatio-temporal and Network Modelling of Diseases'


Tommi Asikainen
Scientific Advice Unit, European Centre for Disease Prevention and Control (ECDC), Stockholm

Future disease challenges in Europe - where modelling is needed
slides - 1.5 MB ppt]

A number of diseases need more attention, these do not have to be the most studied ones at the moment like influenza, HPV and emerging infections. Many EU member states are for example in need of advice on introducing a vaccine against varicella into existing vaccination programs. They need to evaluate the impact of this intervention. Tuberculosis has been around for a while but extremely little modelling has been produced; there are many new treatments in the pipeline. The effect of improving screening of migrants from highly endemic tuberculosis countries is highly requested by health authorities, especially since these can start new disease clusters in the new country. This talk will be followed by a group discussion on identifying a `Top 10' of future modelling challenges.

Modelling as a tool for public health: role and structure of European Union wide networks
slides - 2.2 MB ppt]

There are a number of finished or ongoing research projects in Europe dealing with modelling. These are financed through the Commissions FP6 and FP7 programs. The differences between these will be shown and possibilities to increase public awareness of these projects. We mention the need for an European wide network of modellers, what it could do and possibilities for providing training on a European level.

Frank Ball and David Sirl
School of Mathematical Sciences, University of Nottingham

Network epidemic models with two levels of mixing
slides - 560 KB pdf]

This talk considers two extensions of the standard network SIR (susceptible-infective-removed) epidemic model to include important real-life features, whilst retaining mathematical tractability. The first model incorporates casual contacts, i.e. with people chosen uniformly at random from the population, and the second includes local contacts by way of a household structure. For each model we discuss the calculation of a threshold parameter which determines whether a major outbreak is possible and then consider the probability of such a major outbreak and the expected final size of the epidemic in the event that a major outbreak occurs. Although these results are asymptotic (as the population size tends to infinity), simulation studies indicate that these results provide good approximations for moderately sized finite populations. For the model incorporating household structure we also consider the effect of vaccination according to several different vaccine allocation strategies.

The first part of the talk is based on joint work between Frank Ball and Peter Neal, and the second part on joint work between Frank Ball, David Sirl and Pieter Trapman.

Iain Barrass
Health Protection Agency, Porton Down, UK

Modelling world-wide disease spread: a case for using different spatial scales
slides - 530 KB pdf]

With the threat of international spread of infectious diseases it is hard to consider epidemiological models for a single country in isolation of others. For a UK research group there is a wealth of demographic and health-care data at the UK/EU-level but this does not carry over to the rest of the world. At the extreme level, individual-based models have a single spatial scale but meta-population models have a natural spatial scale based on the data available. Here we would like to discuss how the various spatial scales available to us for a global disease model can be best handled.

Sheila Bird
MRC Biostatistics Unit, Cambridge, UK

Public health and policy issues on illegal drugs use
slides - 180 KB ppt]

I'll comment on:
a) Drugs and statistical science in the 21st century: match-making.
b) Occupational mandatory drugs tests by weeday: prisoners versus privates!
c) Bayesian capture-recapture studies on injection drug users, and UK injectors' drugs-related death rates: missing targets
d) need for formal experiments in criminal justice: court-based randomization in theory versus practice
e) judicial counting!

Maroussia Bojkova
Department of Probability, Operational Research and Statistics. Sofia University, Bulgaria

On age-dependent branching models for surveillance of infectious diseases controlled by additional vaccination
slides - 775 KB pdf]

Vaccination programmes are one of the most effective ways of controlling infectious diseases. Local elimination is the necessary precursor of global eradication, and also represents a desirable public health objective in its own right. Elimination, on the other hand, is the interruption of sustained endemic transmission, which may be achieved by the maintenance of a high level of vaccination coverage. The aim of this study is to analyze the proportion of susceptible individuals that has to be extra-vaccinated in case of fast emerging infectious disease, so that the spread cannot lead to large-scale epidemics.

To this end, the epidemics is modeled through an age-dependent branching process, appropriate for diseases with incubation period and allowing different levels of transmission rates. We study the properties of the time to extinction of an infection, depending on the proportion of the immune individuals into the population. From these results, we suggest a vaccination policy to have the epidemic ceased before a given period of time for a given mean number of contacts.

Vern Farewell
MRC Biostatistics Unit, Cambridge, UK

The Use of Auxiliary Information to Deal with Informatively Missing Data
slides - 110 KB pdf]

Informatively missing or observed data present significant inferential challenges. Structures to characterize observation processes have been suggested, perhaps the most well-known being that associated with the terms, missing completely at random, missing at random and missing not at random. These terms are sometimes further extended to incorporate covariate dependence. To make use of such structures for inference, significant assumptions are usually required. If there is auxiliary information that is closely linked to the observation process, then specific and plausible assumptions may be of particular value. Three examples of this are considered.

Neil Ferguson
Division of Epidemiology, Public Health and Primary Care, Imperial College London

Model complexity: holding back the simulation tide

I shall talk about the gap opening up between the 'agent-based' approach to models (e.g. EpiSims and several others) and the traditional 'minimalist' philosophy, why the audience (who I know will be in the latter camp) should care about this gap and how we might bridge it - which in my view is by more rigorously understanding of the effects of structural assumptions embedded in models and a greater emphasis on rigorous parameterisation. It is also about standing up for reductionism. I may throw in a few other remarks about frequency-dependent infection terms and the fact that many epidemic data sets have far less of a signature of exponential growth than one would expect (even using simulation models).

Matt Ferrari
Center for Infectious Disease Dynamics, Pennsylvania State University.

Spatial patterns on the edge of dynamic stability: measles in the Sahel
slides - 7.8 MB ppt]

Public health and vaccine policy for measles in the Sahel is faced with both logistical and dynamical challenges. Practically, there are powerful constraints on distribution of vaccine and access to care that make the application of uniform strategies a challenge. Dynamically, strong seasonal forcing and high birth rates lead to locally unstable outbreak dynamics. Consequently, large scale regional persistence of measles depends on spatial coupling among communities across huge areas and strong demographic and seasonal gradients. Understanding these spatial dynamics and their implications for regional persistence is key to developing effective public health policy.

Krista Gile
Dept of Statistics, Univ of Washington

Using link-tracing data to inform epidemiology
slides - 820 KB pdf]

A framework for principled statistical network modeling from data from link-tracing designs has been developed by Handcock and Gile (2008). In this talk, we highlight the strengths and limitations of their approach as related to data collection mechanisms of specific epidemiological interest. We briefly introduce an extension to data collected through Contact Tracing, and discuss its limitations. Most of the talk is focused on data collected through Respondent-Driven Sampling (RDS). We introduce RDS and its current estimators, and illustrate limitations of this approach. We then introduce a new RDS estimator based on the fitting of a social network model, and illustrate its superior performance in cases where standard RDS assumptions are not met. This is joint work with Mark Handcock.

Nele Goeyvaerts
Center for Statistics, Hasselt University, Belgium

Elucidating age-specific differences in susceptibility and infectiousness for airborne infections from data on social contacts and serological status
(with Niel Hens, John Edmunds, Marc Aerts and Philippe Beutels)
slides - 2.2 MB pdf]

In order to estimate transmission parameters for airborne infections, one usually relies on estimating 'Who Acquires Infection from Whom'-matrices by combining serological data with assumptions on social mixing behavior. Recently a new approach has emerged in using surveys on social contact patterns. The multi-country contact survey of POLYMOD allows us to estimate rates of making a certain type of contact with high transmission potential.

In five European countries, a seroprevalence survey was conducted for parvovirus B19. For each country, a 'contact surface' is estimated from the contact survey using a bivariate smoothing approach. The age-specific transmission rates are disentangled into the product of two age-specific variables: the contact rate and a proportionality factor. The latter might reflect age-specific differences in characteristics related to susceptibility and infectiousness. Then, making use of the mass action principle and assuming a parametric model for the proportionality factor, maximum likelihood estimates are obtained from the serological data.

Peter Grove
Department of Health, London

Within Pandemic Forecasting in the UK: Plans for nowcasting, short and long term forecasting in an influenza pandemic and the experience gained from exercises
slides - 540 KB ppt]

The talk will describe plans in the UK for nowcasting, short and long term forecasting during an influenza pandemic. The reasons why "within pandemic" forecasting is considered essential to the management of a pandemic in the UK will be discussed. The talk will also cover the systems being put in place to carry out the analysis and those for reporting the results to the highest levels of government. A number of exercises considering the use surveillance data and modelling in a pandemic have been undertaken in the UK and the talk will also consider how the results of these exercises have influenced planning.

Mark Handcock
Dept of Statistics, Univ of Washington

Modeling Networks from partially-observed network data
slides - 380 KB pdf]

Most inference for network models assumes that the presence or absence of all possible links is observed, that the information is completely reliable, and that there are no measurement (e.g. recording) errors. This is clearly not true in practice, as much network data is collected though sample surveys. In addition even if a census of a population is attempted, individuals and links between individuals are missed (i.e., do not appear in the recorded data). We first address the case of missing data in networks. Using an example of data from the National Longitudinal Study of Adolescent Health, we develop a conceptual and computational approach to fitting models to networks with missing data. We then develop a similar approach for sampled network data, including data sampled through link-tracing sampling designs. We illustrate the validity of this approach with simulation samples from a known complete network. This is joint work with Krista Gile.

Valerie Isham
Department of Statistical Science, University College London

Epidemics and rumours on networks
slides - 800 KB pdf]

The SIR model is a special case of a more general rumour model in which there is an extra interaction. Thus, not only does an ignorant (susceptible) contacted by a spreader (infective) become a spreader, and spreaders may "forget" the rumour and become stiflers (removals), but also spreaders will become stiflers if they attempt to spread the rumour to a spreader or stifler (who has already heard it). In this talk, I will describe work in progress on rumour and SIR models that looks at a) the effect of the population size on thresholds, and b) the effect of network structure.

Neils Keiding
Dept. of Biostatistics, Inst. of Public Health, University of Copenhagen

Influenza in Denmark 1918: three contrasting analyses
slides - 460 KB pdf]

This is a a little story put together from three recent papers on the Spanish Flu in Denmark 1918. One is a mainstream J.Inf.Dis. paper by Viggo Andreasen et al. (2008) calculating R0 for the two waves and speculating on the virology. The second is a fascinating new demographic twist on the old competing risks calculations, presented by Canudas-Romo and Erlangsen at the Population Association of America meeting in April 2008, with indications of 'harvesting', i.e. in Denmark the flu mainly killed weak people that would have died anyway from other causes. The third studies both incidence (which is quite rare for this literature) and mortality more descriptively, authored by our Ph.D.student Ida Kolte and her advisors (including myself) and to appear in Scand.J.Inf.Dis. later this year.

Eben Kenah
Departments of Biostatistics and Global Health, University of Washington

Network-based targeting of interventions
slides - 870 KB pdf]

The final outcomes of SIR models in closed populations can be analyzed using a semi-directed random network called the epidemic percolation network (EPN). The epidemic threshold corresponds to the emergence of a giant strongly-connected component (GSCC) in the EPN. Analytic results from fully-mixed models and simulation results from network-based models both strongly suggest that targeting interventions to nodes in the GSCC is a much more efficient method of reducing the probability and final size of epidemics than standard targeting methods. However, the precise properties by which nodes in the GSCC should be targeted remains an open question.

Mirjam Kretzschmar
Julius Centre for Health Sciences & Primary Care, University Medical Centre, Utrecht.

Comparison of network models for STI transmission and intervention: how useful are they for public health?
slides - 310 KB ppt]

Individual based network models have been used by different research groups to analyse screening strategies for chlamydia infections. We compared the performance of three models based on similar principles and found that for the same screening scenarios the model outcomes displayed large differences. We analysed the reasons for those differences. This analysis can be a starting point for discussing the problem of validation and parameter estimation for complex network models.
(more - extended abstract in Word format)

Steven Leach
Health Protection Agency, Porton Down, UK

European demographic and movement data for modelling
(with Philip Sansom, Iain Barrass, Ian Hall)
slides - 6.6 MB ppt]

The construction and use of an infectious disease model depends both on the question(s) that needs to be addressed and on the reliability and completeness of the data available for parameterisation and °»validation°… (e.g.: epidemiological, sociological, disease-specific, and demographic data). These two issues need particular consideration with respect to population demographic and movement data when determining the spatial resolution (scale) and geographic coverage (extent) that would be appropriate for an effective model. Various EU-funded projects have sourced and assessed such data at sub-country, country, European and international scales and these data will be briefly reviewed. Not unexpectedly, as extent is increased they tend to get much less reliable and complete (and also less coherent) at finer spatial scales. This means that whilst data for a single country can often be highly spatially resolved and therefore useful for more °»local°… questions, this cannot necessarily be maintained as the extent has to be increased to include a wider geographic context. Without more comprehensive international data are there approximations that would address this problem satisfactorily?

Alun Lloyd
Mathematics Department, North Carolina State University (Raleigh).

Novel Control Strategies for Vector Borne Diseases: New Challenges for Modellers
slides - 6.3 MB pdf]

Several large projects are exploring the use of novel strategies, based on genetic modification of mosquitoes, to control vector-borne infections such as dengue or malaria. Modellers are playing a significant role in these projects. I shall discuss some of the genetic approaches and the accompanying modelling work, in which spatial structure and other heterogeneities are key considerations.

Malwina Luczak (with Andrew Barbour)
Department of Mathematics, London School of Economics

Laws of large numbers for epidemic models with countably many types
slides - 1.5 MB pdf]

In modelling parasitic diseases, it is natural to distinguish hosts according to the number of parasites that they carry, leading to a countably infinite type space. Proving the analogue of the deterministic equations, used in models with finitely many types as a `law of large numbers' approximation to the underlying stochastic model, has previously either been done case by case, using some special structure, or else not attempted. In this paper, we prove a general theorem of this sort, and complement it with a rate of convergence in the L_1-norm.

Eduardo Massad
Faculdade de Medicina, University of Sco Paulo

Scale-Free Network of Dengue in Singapore
slides - 510 KB pdf]

In this work we show that the dengue epidemic in Singapore tends to organize itself into a scale-free network of transmission as the outbreak progressed from 2000 to 2005. This scale-free network of cluster comprised geographical breeding places for the aedes mosquitoes, acting as super-spreaders of the infection. The geographical organization of the network was analysed by the corresponding distribution of weekly number of new cases. Therefore, our hypothesis is that the time distribution of dengue cases reflects the geographical organization of a transmission network, which evolved towards a power law as the epidemic intensity progressed from 2000 until 2005.

Johannes Mueller
Centre for Mathematical Sciences, TU Munich
Institut fur Biomathematik und Biometrie, GSF Munich

What do data from contact tracing tell us?
slides - 130 KB pdf]

Contact tracing is a control method for infectious diseases that is believed to be quite effective. If an infected person is noticed (the index case) one tries to find more infected persons via the contact history of the index case. As it is quite simple to keep track especially of the number of detected cases per index case, it is intriguing to ask about the information these data contain w.r.t. rates, reproduction number or contact structure.
By now, one has basically three approaches:
(1) a phenomenological approach that incorporates contact tracing as a linear or nonlinear term in a deterministic framework, where this term is not derived by a submodel on the micro-level;
(2) by means of moment closer method for individual based stochastic models;
(3) the third approach formulates the infectious process with contact tracing as a nonlinear branching process. Methods have been developed to analyse this process in the onset of the disease.
In this talk, we take up the third approach and focus on the endemic state of an SIS model. As dependencies due to contact tracing as well as dependencies due to the high prevalence of diseases are present (I-I contacts cannot be neglected in the endemic state), the analysis is not straight forward. We propose a preliminary method, partially based on heuristic arguments. As we assume a relatively simple model (SIS model), we focus on the estimating rates (or better: combination of rates). We cannot tell something about the contact structure, though this is a quite interesting problem. We discuss if this method can be extended in this direction.

Nico Nagelkerke
United Arab Emirates University, Al Ain

Heterogeneity in host HIV susceptibility as a potential contributor to recent HIV prevalence declines in Africa
slides - 810 KB ppt]

Background. HIV prevalence has recently declined in several African countries, and prior to this the risk of HIV acquisition per unprotected sex contact also declined in Kenyan sex workers. Heterogeneity in HIV host susceptibility might underpin both of these observations.
Methods. A compartmental mathematical model was used to explore the impact of heterogeneity in susceptibility to HIV infection on epidemic behavior.
Results. Substantial heterogeneity in susceptibility to HIV infection may lead to an epidemic that peaks and then declines due to a depletion of the most susceptible individuals. This effect was most notable in high-risk groups such as female sex workers, and was consistent with empirical data.
Discussion. Declines in HIV prevalence may be caused by heterogeneity in host HIV susceptibility. This heterogeneity confounds the ability to attribute HIV epidemic shifts to specific interventions.

Philip O'Neill
School of Mathematical Sciences, University of Nottingham

Relating Models to Data: a review
slides - 850 KB ppt]

In this talk we cover topics such as (i) the purpose of modeling (ii) the reality of data (iii) recent developments in parameter estimation (including both computationally intensive methods and others) (iv) recent developments in model choice, all with examples/applications.

Philip O'Neill and Theodore Kypraios
School of Mathematical Sciences, University of Nottingham

Modelling and data analysis for antibiotic-resistant pathogens in healthcare settings
slides - 1.7 MB pdf]

High-profile hospital "superbugs" such as MRSA, VRE etc have a major impact on healthcare within the UK and elsewhere. Despite enormous research attention, many basic questions concerning the spread of such pathogens remain unanswered. Here we demonstrate how biologically-meaningful stochastic transmission models that overcome unrealistic assumptions of methods which have been previously used in the literature can be used in conjunction with computationally-intensive statistical techniques to address specific scientific hypotheses of interest, using detailed data from hospital studies. The extent to which the data support specific scientific hypotheses is investigated by considering and comparing different models. Finally, we will also indicate current and future research directions in this area.

Nelson Onyango
Technical Univ of Munich

Optimal Vaccination Strategies in Periodic Settings
slides - 390 KB pdf]

Vaccination of childhood diseases has failed in many countries due to ineffective vaccination strategies. Many countries have vaccination effort spread homogenously over time. This has been shown to be less effective, due to quasiperiodic disease outbreaks in reported even in developed countries such as USA, Israel, and the UK. Pulse vaccination or discrete time vaccination has been recommended and used, e.g. in Brazil, with success.

Many infectious diseases have periodic contact patterns. One obvious reason is the school year, but also seasonal effects influence the force of infection in a periodic manner. The standard approach for periodically driven systems is Floquet-theory. This theory, however, is basically suited for systems where all time scales are of the same order. Especially in childhood diseases, this assumption is not met: an outbreak of measles in a school, say, may last only a few weeks.

In this talk we discuss two different stability measures, based on Floquet theory on the one hand, and on singular perturbation theory on the other. The relation to the time scale of epidemics is considered. Furthermore, we touch on the resulting problem of different optimization problems for control of epidemics by vaccinations in the different settings. We show the existence of optimal vaccination patterns. The solution of the corresponding optimization problems, however, is still ongoing work.

Mick Roberts
Inst. of Information and Mathematical Sciences, Massey University, New Zealand.

Seasonal influenza in New Zealand
slides - 4.2 MB pdf]

Winter epidemics of influenza are an annual event in temperate countries. Three variants of the virus are currently responsible: the influenza A subtypes H1N1 and H3N2, and influenza B. Recovery from infection with one variant appears to suppress a second infection with the same variant in the same season, and the lack of complete cross-protection results in selection for (sub)variants more able to evade the immune response. New Zealand experiences influenza epidemics every Southern Hemisphere winter, with the highest incidence during June and July. Immunisation has been available free of charge to those over 65 years old since 1997, and to other at-risk groups since 1999, and has been associated with a decrease in mortality from influenza.

We have developed and analysed a model for three co-circulating influenza variants infecting an isolated community with vaccination. Key assumptions are that influenza is introduced annually from an external source, mutation within variants occurs between successive introductions, drift within the epidemic season is negligible; and that there is a degree of cross-immunity between sub-types within the same season but not between seasons. Preliminary results from the model are presented.

Lisa Sattenspiel
Department of Anthropology, University of Missouri-Columbia

The potential significance of co-circulating pathogens on patterns of spatial spread: Insights from the historic record
slides - 1.5 MB pdf]

The majority of spatial epidemic models address the spread of a single infectious disease epidemic. Yet often in real populations multiple disease strains or different pathogens are circulating through a population simultaneously or close in time. I present here data on the geographic spread of the 1918-19 flu epidemic and a 1915-16 measles epidemic in Newfoundland to illustrate possible interactions between the epidemics that may have affected observed patterns of spatial spread. I also describe other epidemics known to have spread on the island during the early 20th century. Results from analyses testing the presence of interactions between the flu and measles epidemics will be presented. These results provide a springboard from which to discuss the utility of developing more complex models that take into account multiple pathogens.

Ake Svensson
Department of Mathematical Statistics, Stockholm University

Non-parametric estimation of transmission functions in emerging epidemics
slides - 160 KB ppt]

Assumptions about when transmission of an infection takes place are essential in epidemic modelling. Today many epidemic models are based on the concept of generation times. Popular assumptions are that the duration of latency or infectious times are exponentially, gamma, log-normal or Weibull distributed. The purpose of the talk is to investigate to what extent it is possible to infer characteristics of the generation-time distribution from observations of epidemic trees or epidemic curves.

Pieter Trapman
Department of Mathematics, Free University of Amsterdam
and Faculty of Vetinary Medicine, Utrecht University

Is R0 compatible with spatial epidemics? - new results from long-range percolation
slides - 1 MB pdf]

I will consider long-range percolation on Zd, as a model for the generation based spread of a spatial epidemic. In this model, the probability that an infectious individual contacts an individual at distance r during its infectious period, is given by p(r) and is independent of all other contacts made in the population. In most cases, |Bk|, the number of individuals that are within k "infection-generations" from the origin, will not grow exponentially in k, which implies that R0, in its usual interpretation, is not a useful concept for most spatial epidemics. However, some functions p(r) exist, for which, as k tends to infinity, lim P(a1 < |Bk|1/k < a2) = 1, and R0 might be useful. Recently long-range percolation has been used in modeling the well documented spread of plague among great gerbils in Kazakhstan.

Jacco Wallinga
Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht
and Centre for Infectious Disease Control Netherlands, Epidemiology and Surveillance Unit National Institute of Public Health and the Environment (RIVM)

Who infected whom? Estimation of infection trees, generation intervals and local network structure
slides - 700 KB pdf]

The key variables determining spread of infection are the reproduction number and the generation interval. We propose a method to reconstruct likely infection trees from partially observed infectious disease outbreaks, and use these reconstructed infection trees for joint estimation of the distribution of generation intervals and reproduction numbers. We explore how the infection trees, generation intervals and reproduction numbers are affected by the local structure of the contact network.

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27th October 2008