DIMACS Working Group on Spatio-temporal and Network Modeling of Diseases III

October 21 - 25, 2008
Tubingen, Germany

Martin Eichner, Tubingen University, martin.eichner at uni-tuebingen.de
Nina Fefferman, DIMACS, nina.fefferman at tufts.edu
Valerie Isham, University College, London, valerie@stats.ucl.ac.uk
Alun Lloyd, North Carolina State University, alun_lloyd at ncsu.edu
Denis Mollison, Heriot-Watt University, Edinburgh, denis at ma.hw.ac.uk
Presented under the auspices of the Special Focus on Computational and Mathematical Epidemiology.


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

Title: The top 10 future disease threats - (Future disease challenges in Europe where modelling is needed)

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.

Second Talk:

Title: Modelling as a tool for public health: role and structure of European Union wide networks

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

Title: Network epidemic models with two levels of mixing

The work with David extends standard network models by also partitioning the population into households with additional spread within households. The work with Pete extends them by allowing individuals to make additional "casual" contacts (i.e. with individuals chosen uniformly at random from the whole population).

Iain Barass, Health Protection Agency, Porton Down, UK

Title: Modelling world-wide disease spread: a case for using different spatial scales

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

Title: Public health and policy issues on illegal drugs use

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!

Vern Farewell, MRC Biostatistics Unit, Cambridge, UK

Title: The Use of Auxiliary Information to Deal with Informatively Missing Data

Significant assumptions are usually required to deal with informatively missing data. A brief introduction is given to this problem and to situations where the use of auxiliary information may be useful. An example of disease progression in Hepatitis C patients is presented in more detail. The use of routine clinical data is shown to allow the estimation of a partially hidden Markov model for liver damage that is defined by biopsy and therefore not observed at all clinic visits.

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

Title: 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.

Title: Spatial patterns on the edge of dynamic stability: measles in the Sahel

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, Univ of Washington

Title: Using link-tracing data to inform epidemiology

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.

Peter Grove, Department of Health, London

Title: Within Pandemic Forecasting in the UK: Plans for nowcasting, short and long term forecasting in an influenza pandemic and the experience gained from exercises.

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.

Nele Goeyvaerts, Center for Statistics, Hasselt University, Belgium

Title: 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)

Whereas estimating transmission parameters for non-sexual close contact infections hitherto usually relied on estimating so-called 'Who Acquires Infection from Whom'-matrices by combining serological data with assumptions on how people interact, recently new approaches emerged based on using surveys (rather than assumptions) on social contact patterns. These surveys used conversations with and without touching and their duration as proxies for effective contacts, i.e. contacts with transmission potential, and the new approaches have shown better predictiveness on observed age-specific serological profiles than the previous "standard" approach. The work presented here disentangles the age-specific transmission rates into the product of two age-specific variables: the contact rate and a proportionality factor. This age-specific proportionality factor likely reflects age-specific differences in characteristics related to susceptibility (eg, age-specific changes in immunodeficiency where very young and the elderly are more susceptible) and infectiousness (eg, age-specific changes in viral excretion, where young children are more infectious than adults). We illustrate these aspects using data on parvovirus B19 serology from various European countries, as well as pre-vaccination data on a range of different airborne infections from the UK. The elaborations and discussions are focused on the desirability of using an age-specific rather than a constant proportionality factor.

Mark Handcock, Dept of Statistics, Univ of Washington

Title: Modeling Networks from partially-observed network data

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 develop the conceptual and computational theory for inference based on sampled network information, and present some applications. This is joint work with Krista Gile.

Valerie Isham, Department of Statistical Science, University College London

Epidemics and rumours on networks

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

I think I might well put together a little story on 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, Department of Epidemiology, Harvard School of Public Health.

Title: Network-based targeting of interventions

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, University Medical Centre, Utrecht

Title: Comparison of network models for STI transmission and intervention: how useful are they for public health?

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.

Steven Leach, Health Protection Agency, Porton Down, UK

Title: European demographic and movement data for modelling

Alun Lloyd, North Carolina State University (Raleigh).

Title: Novel Control Strategies for Vector Borne Diseases: New Challenges for Modellers

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, Department of Mathematics, London School of Economics

Title: Laws of large numbers for epidemic models with countably many types

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

Title: Scale-Free Network of Dengue in Singapore

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

Title: What do data from contact tracing tell us?

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

Title: Heterogeneity in host HIV susceptibility as a potential contributor to recent HIV prevalence declines in Africa

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.

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

Title: Relating Models to Data: a review

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.

Second Talk

Title: Modelling and data analysis for antibiotic-resistant pathogens in healthcare settings

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 can be used in conjunction with computationally-intensive statistical techniques to address specific scientific hypotheses of interest, using detailed data from hospital studies, and indicate current and future research directions in this area.

Nelson Onyango, Technical Univ of Munich

Title: Optimal Vaccination Strategies in Periodic Settings

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 United Kingdom. Pulse vaccination or discrete time vaccination has been recommended and used e.g., in the case of Brazil with success.

Many infectious diseases have periodic contact pattern. 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 not met: an outbreak of measles in a school, say, may last only 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 hand. The relation to the time scale of epidemics is considered. Furthermore, we touch 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.

Title: Vaccination against seasonal influenza in New Zealand

.. it could turn out to be part review of flu models and part NZ vaccination policy. I have data!

Lisa Sattenspiel, Department of Anthropology, University of Missouri-Columbia

Title: The potential significance of co-circulating pathogens on patterns of spatial spread: Insights from the historic record.

I have lots of interesting data from Newfoundland and so I can pose some stimulating questions about the potential value of setting models for a particular infectious disease within a more realistic context. Unfortunately, I don't think I will have a working model that can address this \& I have a prototype agent-based model, but it just has agents moving around randomly on the space. We are still dealing with computer hassles and limits to our programming knowledge so it's hard to predict how far we will get by October, but it is likely to be no further than modeling a single disease with a somewhat realistic population structure.

Gianpaolo Scalia-Tomba, Department of Mathematics, University of Rome Tor Vergata

Title: The statistics of generation times in epidemic spread models

The concept of generation time of an infectious disease has an "innocent" definition, viz. the time from the moment one person becomes infected until that person infects another person. This concept is similar to the demographic concept "generation gap", with new infections replacing births in a population. However, a theoretical analysis of the statistics of generation times in simple stochastic model for disease spread show that biases, usually not considered in the literature arise.

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

Title: On age-dependent branching models for surveillance of infectious diseases controlled by additional vaccination

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.

Ake Svensson, Department of Mathematical Statistics, Stockholm University

Title: Non-parametric estimation of transmission functions in emerging epidemics

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

Title: Is R0 compatible with spatial epidemics? - new results from long-range percolation

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)

Title: Who infected whom? Estimation of infection trees, generation intervals and local network structure

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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Document last modified on September 29, 2008