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Timetable (IDDW01)

Infectious Disease Dynamics

Monday 19th August 2013 to Friday 23rd August 2013

Monday 19th August 2013
08:30 to 09:20 Registration
09:20 to 09:30 Welcome by John Toland, Director of the Institute INI 1
09:30 to 10:00 D Mollison (Heriot-Watt University)
Setting the scene
I shall try to set in context the 6-month Epidemic Models programme that took place in 1993 in the Newton Institute's first year; and to outline how we then tried to identify future directions for research.

Related Links: • - speaker's web page

10:00 to 10:30 V Isham (University College London)
Stochastic methods: past, present and future. Part I
This talk aims to outline the position as regards stochastic models at the time of the first Epidemic Models programme at the INI in 1993, describing some of the issues that were identified then as future research challenges, to indicate some of the advances that have been made in the intervening 20 years, and to point to areas for further work.
10:30 to 11:00 P Trapman (Stockholm University)
Stochastic Methods - past, present and future
We will talk about the development of stochastic methods in the modelling of infectious diseases since 1993, the current state and perspectives for the coming 20 years.
11:00 to 11:30 Morning Coffee
11:30 to 12:00 M Roberts (Massey University)
Deterministic models: twenty years on. I. Spatially homogeneous models
In this talk I will review deterministic epidemic models that do not have an explicit spatial structure. The most ubiquitous of these is the SIR model, which is a special case of the Kermack-McKendrick model. Many properties of these models can be deduced from the well-known basic reproduction number, $\mathcal{R}_0$. Following the introduction of a typical primary infectious case in an otherwise susceptible population, $\mathcal{R}_0$ measures the expected change in prevalence from one infection generation to the next. There is a one-to-one correspondence between $\mathcal{R}_0$ and $r$, the Malthusian parameter or initial rate of increase in infection incidence, directly linking generation time and chronological time. The value of $\mathcal{R}_0$ determines the final size of the epidemic, which is independent of temporal dynamics. It also provides a measure of the control effort required to prevent an epidemic, or to eliminate an existing infection from a population. Where the modeled populations are structured, for example by sex, species, or groups at high risk of infection, $\mathcal{R}_0$ can be determined from the Next Generation Matrix. However, it is not always sensible to average over different host types or states at infection, so an alternative threshold quantity the Type Reproduction Number $\mathcal{T}$ has been defined. The value of $\mathcal{T}$ provides a measure of the effort required when control is targeted. For macroparasite life cycles there is only one state at infection, as pathogen development proceeds through prescribed stages. Here, $\mathcal{R}_0$ measures the change in parasite population density from one infection generation to the next. Finally, in periodic environments the number of secondary cases depends on the timing of the primary case. Careful averaging is then necessary, and the value of $\mathcal{R}_0$ can be determined as the spectral radius of the Next Generation Operator.
12:00 to 12:30 L Pellis (Imperial College London)
Deterministic models: twenty years on. II. Spatially inhomogeneous models
Building on the previous talk, I will provide an overview of recent methodological developments for deterministic models of infection spread in populations with an explicit spatial structure or, more generally, models in which local depletion of susceptibles makes standard techniques for single and multitype models fail. In this case, linearising the dynamics becomes non-trivial even in the early phases of the epidemic, with repercussions on the definition of $R_0$ and the real-time growth rate. In addition, local scale effects, which typically involve small number of individuals, challenge the very nature of deterministic models. Although it can be argued that fundamental advances have been achieved through the use of stochastic models, deterministic techniques have not disappeared and are still key tools for capturing or approximating the average behaviour of large-scale systems. In this respect, I will discuss pair formation models, network models and moment-closure approx imations, models with household or multiple levels of mixing, metapopulation and spatial models (e.g. kernel-based, gravity and reaction-diffusion models). I will highlight the motivations behind their development, their strengths and limitations, as well as their successful applications in practical contexts. I will briefly conclude by commenting on the problem of model comparison and selection and suggesting where I believe the future methodological challenges for deterministic epidemic models lie.
12:30 to 13:30 Lunch at Wolfson Court
13:30 to 14:00 I Longini (University of Florida)
Mathematical Models for the Control of Infectious Diseases With Vaccines
In this talk, I will present the general formulation for the control of infectious diseases with vaccines. I will then present a number of examples including the control of influenza, cholera and dengue.
14:00 to 14:30 S Cauchemez (Imperial College London)
Twenty years of statistical methods for the study of infectious diseases
I will review 20 years of statistical methods for the study of infectious diseases, commenting on successes and failures. I will discuss areas of statistical inference where further developments are needed.
14:30 to 15:00 B Grenfell (Princeton University)
Linking models and data: Sense and Susceptibility
We briefly review successes and challenges in capturing dynamics of acute infections based on incidence time series. We conclude that systematic collection of susceptibility information via longitudinal serology would greatly facilitate both model inference and design of control programs.
15:00 to 15:30 J Metcalf (University of Oxford)
Linking models and data for infectious disease dynamics: rubella as a case-study
Co-authors: Bryan Grenfell (EEB, Princeton), Ottar Bjornstad (CIDD, Penn State), Justin Lessler (Bloomberg School of Public Health, Johns Hopkins), Andy Tatem (Geography, Southampton), Amy Wesolowski (Engineering and Public policy, Carnegie Mellon), Caroline Buckee (School of Public Health, Harvard) Following a general preamble on linking models and data from Bryan Grenfell; we move to a specific example with rubella, a directly transmitted and completely immunizing infection. It manifests as a mild disease in children, but infection of women during the first trimester of pregnancy can lead to birth of a child with Congenital Rubella Syndrome (CRS), which can include deafness, blindness and mental retardation. Since vaccination will raise the average age of infection, and thus concentrate infection into women of child bearing age, vaccination short of thresholds required for elimination may increase the burden of CRS. The relatively simple epidemiology of this infection means that generic models linking demography and epidemiology can take us a long way in terms of understanding the minimum levels of vaccination required to ensure a reduction in the CRS burden. However, increasingly resolved data-sets indicate the importance of stochastic dynamics for the burden of this infection. Here, I detail some of these patterns, and then point to areas where novel datasets may be essential to developing our ability to predict the consequences of rubella vaccination, including quantifying spatial heterogeneity in vaccination coverage and understanding human movement.
15:30 to 16:00 Afternoon Tea
16:00 to 17:00 J Wood & J Gog (University of Cambridge)
The evolution of pathogen evolution
Starting from the writeup from the working groups from the 1993 INI meeting, we explore how the modelling of pathogen variability and evolution has developed in the last 20 years. We focus particularly on antigenic evolution, such as for influenza, and the role of pathogen evolution in the emergence of zoonotic infections. Finally, we propose that current technological advances are offering future challenges in modelling pathogen evolution.
17:00 to 18:00 D Klinkenberg & M de Jong ([Universiteit Utrecht/Wageningen University])
Veterinary epidemiology: where mathematical modellers , biologists, animal scientists, and veterinarians (should) meet
Infectious disease problems in farmed animals are studied by mathematical modellers and veterinary epidemiologists, often without optimal use of each other’s proficiency. Quality of mathematical models and acceptance by non-modelling epidemiologists and veterinarians should profit from using all knowledge that is present in biological and veterinary communities. More than in other areas of infectious disease epidemiology, veterinary epidemiology allows for detailed observational studies with repeated measurements and for experimental approaches. We will discuss developments in veterinary epidemiological modelling, focussing on heterogeneity and data analysis, identified in the 1993 Newton Institute meeting on Epidemic models (Mollison, 1995). Heterogeneity appeared important in modelling: (i) Bovine Spongiform Encephalopathy (BSE), with large variation in incubation times and initially very uncertain predictions of incidence; (ii) Foot-and-Mouth Disease (FMD), with variation in susceptibility, infectivity, and clinical outcome in different animal species; (iii) Bluetongue, with spatial heterogeneity in vector abundance, to be extracted from vector trapping data and remote sensing; (iv) Avian Influenza, with interactions between ecology of migratory birds, contact patterns of poultry, evolution of strains, and the risk of a human pandemic. Experimental data have been used to quantify BSE incubation times and transmission heterogeneity between animal species in FMD, to address the scaling of contact rates between different settings (as in De Jong et al, 1995), and to study environmental transmission. For the future, we foresee the use of more genomic data to address heterogeneities, both in pathogens and hosts. We advocate use of mechanistically based decision rules to complement predictions by detailed simulations or complex mathematical models. These rules will facilitate the dialog with non-modellers if they have a biological interpretation and can be substantiated by data.
18:00 to 19:00 Welcome Drinks Reception
Tuesday 20th August 2013
09:00 to 09:30 T House (University of Warwick)
Epidemics and population structure: One step forward, and two steps back
In general, the incorporation of population structure into epidemic models creates problems of dimensionality for prediction (the `forward problem'). Even for the `simple epidemic' / SI model, complete individual heterogeneity of n individuals leads to a dynamical system whose size grows like 2^n.

There are, however, two `inverse problems' where this curse becomes a blessing: for statistical inference, flat directions in parameter space can become identifiable once more stratification of data is available; and the presence of population structure allows a far wider range of control and mitigation strategies to be compared than are possible in a homogeneous system.

This talk will consider: (i) the generation of predictions from heterogeneous epidemic models without excessive dimensionality; (ii) the use of multiple stratified data sources to resolve statistical questions about the otherwise unidentifiable but epidemiologically important quantities; (iii) informing public health policy on the basis of these considerations. Real-world examples will come from the 2009 H1N1 influenza pandemic.

09:30 to 10:00 M Morris (University of Washington)
Exponential Family Random Graph Models: A data-driven bridge between networks and epidemics
Co-authors: Mark S.Handcock (University of California Los Angeles), David R. Hunter (Pennsylvania State University), Carter T. Butts (University of California Irvine), Steven M. Goodreau (University of Washington), Skye Bender-deMoll (At Large), Pavel Krivitsky (University of Woolongong)

In a small comment on the Mollison, Isham and Grenfell JRSS paper at the end of the Newton Workshop in 1994, I speculated on the potential for an emerging stochastic modeling framework to provide the missing link between network and epidemic modeling. Now, 30 years later, that link is firmly established. In this talk I will briefly summarize the theory of Exponential Family Random Graph Models (ERGMs), a comprehensive statistical framework that makes it possible to estimate generative parameters for network structure from a wide range of data, and simulate static or dynamic networks with the observed features. The talk will cover the extensive software available in the "statnet" related packages on CRAN and highlight some recent applications to epidemic modeling.

Related Links: • - the statnet wiki • - Journal of Statistical Software Volume on statnet (2008) • - A network epidemiology movie

10:00 to 10:30 C Dye (World Health Organization)
Infectious diseases in the changing landscape of public health
Infectious diseases will be eliminated and replaced by chronic, lifestyle diseases as fertility falls, life expectancy increases, and populations grow old. This is the standard story of the epidemiologic transition, but it hasn’t turned out as we imagined. Even the massive effort to contain major infections – especially HIV/AIDS, tuberculosis and malaria – within the framework of the Millennium Development Goals (MDGs) has left much unfinished business. As we approach the 2015 deadline for reaching the MDGs, the selection of a new set of development goals has become a matter for intense debate. In this talk I will consider how the analysis of infectious disease epidemiology and control has influenced, and been influenced by, the changing landscape of public health over the past two decades, and how infections might figure in the post-2015 agenda. Among the topics for discussion will be the domination of the “big three”, the quest for eradication, the failure of health systems analysis, and the place of infection in a new era of sustainable development.
10:30 to 11:00 N Arinaminpathy (Princeton University)
Dollars and disease: developing new perspectives for public health
In addressing current priorities in global health, particularly as embodied by the Millennium Development Goals, there are diverse opportunities for the analysis of infectious disease epidemiology to contribute to policy. Economic factors can play an important role in translating mathematical models to practical realities of policy formulation: for example, linking cost-benefit analysis to mathematical modelling has been key in evaluating and comparing different interventions for infectious disease control.

More broadly, however, changes in economic conditions can also profoundly impact disease transmission, whether in macroeconomic recessions (as in the case of the recent global financial crisis) or in the use of economic levers to facilitate disease control (such as global financing mechanisms). Addressing public health in these contexts – especially for diseases of poverty such as the ‘big three’ – calls for a deeper understanding of the role of economic systems in shaping disease transmission. Here I will survey some recent and ongoing work representing steps in this direction. I will draw on examples from market dynamics, operations modelling and economic recessions, as well as highlighting important questions for future work, aiming to understanding the role of economic systems in public health.

11:00 to 11:30 Morning Coffee
11:30 to 12:00 A Dobson (Princeton University)
Multi-host, multi-parasite dynamics
Co-author: Anieke van Leeuwen (Princeton University)

“The unpredictable and the predetermined unfold together to make everything the way it is.” ? Tom Stoppard, Arcadia

In this talk I'll discuss mathematical and empirical developments over the last twenty years that examine the role that parasites play in natural (non-human) communities of hosts. The organizing theme of the talk is the role that parasite diversity plays in determining the dynamic and geometric structure food webs. I'll organize the talk into four sub-sessions that examine (1) The dynamics of parasites with multiple hosts; (2) Parasites with sequential multiple hosts (3) the dynamics of parasite communities; and (4) the need for a better understanding of the role that host immunity plays in structuring parasite communities.

12:00 to 12:30 J Pulliam (University of Florida)
Embracing the complexities of scale and diversity in disease ecology
12:30 to 13:30 Lunch at Wolfson Court
14:00 to 14:30 P O'Neill (University of Nottingham)
Data and Statistics: New methods and future challenges
We discuss some current work on statistical methodology for infectious disease data (including Bayesian non-parametric inference and model choice), and also draw attention to the challenges of modelling and inference for high-resolution epi-genetic data.
14:30 to 15:00 O Bjornstad (Pennsylvania State University)
Some challenges to make current data-driven (‘statistical’) models even more relevant to public health
There has been enormous progress in parameterizing epidemic models using incidence data in the 20 years since the Newton meeting on Epidemic models. This came about through a combination of computational innovations, model development to embrace critical biological realism, and increasingly resolved incidence data with respect to age, time and space. I will highlight what I think are key challenges to data-driven epidemic modeling to advice future intervention policies. Some critical issues are (i) robust forecasting in the face of rapidly changing demographies and vaccination schedules; (ii) probabilistically projecting possible/probable build-up of ‘susceptible pockets’ in the face of imperfect vaccination programs; and (iii) use nonlinear stochastic modeling to identify all potentially undesirable side-effects of intervention-induced reduction in circulation.
15:00 to 15:30 T Bogich (Princeton University)
Inference pipelines for nonlinear time series analysis applied to an emerging childhood infection
Using the case study of Hand Foot and Mouth Disease (HFMD) in Japan, we distill inference down to atomic, pipe-able plug-and-play methods for time series analysis with state space models. For HFMD, we find evidence for cross protection between two causative agents (EV71 and CA16) and herd immunity, as well as some evidence for reinfection. The inference pipeline method, coupled with cloud computing, provides the opportunity for full Bayesian model comparison to be conducted over a set of more than 3000 of mechanistic models.
15:30 to 16:00 Afternoon Tea
16:00 to 16:30 F Ball (Stockholm University)
Stochastic epidemic modelling and analysis: current perspective and future challenges
Co-author: Tom Britton (Stockholm University)

This talk is concerned with stochastic modelling and analysis of epidemics, and focuses on models for which some analytic progress is possible. We discuss current research in this area and outline some open problems for future work. The first half of the talk, given by Frank Ball, is concerned with the short-term behaviour of emerging epidemics and the second half, given by Tom Britton, is concerned with the long-term behaviour of established epidemics.

16:30 to 17:00 T Britton (Stockholm University)
Stochastic epidemic modelling and analysis: current perspective and future challenges
In the talk we explore how to perform inference when data consists of two sources: 1) temporal outbreak data in a structured community, and 2) sequences of the disease agent from the infected individuals.

We investigate how to perform inference and study how much is gained compared to only having either of the two sources of data.

Wednesday 21st August 2013
09:00 to 09:30 J Drake (University of Georgia)
Early warning signals of critical transitions in infectious disease dynamics
Anticipating infectious disease emergence and documenting progress in disease elimination are important applications for the theory of disease dynamics in changing environments. A key problem is the development of ideas relating the dynamical processes of transmission to observable phenomena. Here, we consider compartmental epidemiological SIS and SIR models that are slowly forced through a critical transition. We derived expressions for the behavior of several candidate indicators, including the autocorrelation coefficient, variance, coefficient of variation, and power spectra of SIS and SIR epidemics during the approach to emergence or elimination and validated these expressions using individual-based simulations. Our results show that moving-window estimates of the candidate indicators may provide useful model-independent signals for anticipating critical transitions in infectious disease systems. Although these leading indicators were highly predictive of elimination, we found the approach to emergence to be more difficult to detect. It is hoped that these results, which show the anticipation of critical transitions in infectious disease systems to be theoretically possible, may be used to guide the construction of online algorithms for processing surveillance data.
09:30 to 10:00 B Halloran (Fred Hutchinson Cancer Research Centre)
Design and Analysis of Vaccine Trials
10:00 to 10:30 M Woolhouse (University of Edinburgh)
Theory and practice of infectious disease surveillance
Surveillance is the first line of defence against infectious disease outbreaks, making the design of effective and efficient surveillance systems an important public health challenge. Both statistical and process models of outbreak dynamics are potentially useful in this context, but there have been relatively few applications of these tools to designing surveillance systems, in marked contrast to the many and influential applications to prevention and control programmes. Here, I review efforts to fill this gap, focussing on the design of so-called ‘smart’ surveillance systems that incorporate knowledge of patterns of risk to target surveillance effort more efficiently. There are several examples where smart surveillance systems have been shown to be considerably more efficient: post-epidemic surveillance for freedom from foot-and-mouth disease (5x more efficient); detection of new infections spreading through a network of hospitals (up to 8x). Designing surveillance systems is more challenging when signal has to be separated from noise. This is important for understanding the impact of vaccination on the detection of H5N1 influenza in poultry or the detection of pandemic influenza in the presence of seasonal influenza. There is an even more difficult problem of identifying novel “events”, e.g. unusual clinical cases or outbreaks due to unrecognised, unexpected or even completely new infectious diseases. This is being addressed by using data reduction methods to provide a benchmark for expected patterns of variation in clinical presentation or outbreak characteristics. Designing smart surveillance systems presents a number of interesting challenges, both in theory and in practice. The take home message from the various studies described here is that model-based approaches have considerable potential to contribute to improving the effectiveness and efficiency of surveillance systems, to the benefit of both human and animal health.
10:30 to 11:00 Morning Coffee
11:00 to 11:30 A Lloyd (North Carolina State University)
Quantifying Uncertainty in Model Predictions
Quantifying uncertainty in a model's predictions is crucial if we are to have faith in those predictions. Uncertainties arise from a number of sources, including uncertainty in the values of the model's parameters (parametric uncertainty), uncertainty in the structure of the model and stochasticity in the model's dynamics. In this talk I will discuss and apply a number of uncertainty quantification (UQ) techniques to simple disease transmission models.
11:30 to 12:00 C Viboud (National Institutes of Health)
Inference of epidemiological dynamics using sequence data: application to influenza
In the past decade, there has been a rapid increase in the availability of high-resolution viral sequence and epidemiological data, combined with developments in statistical and computational methods to simulate and infer the population dynamics of viral infections. Sequence-based approaches have provided key insights into the spatial and temporal dynamics of influenza A viruses in humans. In this talk, we will review and contrast findings from phylogenetic and epidemiologic studies of influenza population dynamics.
12:00 to 12:30 D de Angelis (University of Cambridge)
Multiple Data Sources, Missing and Biased Data
Inferential methods based on multiple data sources are becoming increasingly common in infectious disease epidemiology, to combine heterogeneous, incomplete and biased evidence. We describe a Bayesian approach to evidence synthesis, highlight its ability to incorporate all available information in a single coherent probabilistic model and discuss current challenges in this area.
12:30 to 13:30 Sandwich lunch at INI
13:30 to 15:30 Free/Excursions
18:00 to 19:00 T Korner (University of Cambridge)
Special Lecture at Cambridge Union Society: The Mathematics of Smallpox
Smallpox inoculation was a dangerous procedure to prevent a dangerous disease. Daniel Bernoulli tried to apply mathematics to see if it was worthwhile. His work raises questions which are still pertinent.
19:30 to 22:00 Conference Dinner at Cambridge Union Society hosted by Cambridge Dining Company
Thursday 22nd August 2013
09:00 to 09:30 O Diekmann (Universiteit Utrecht)
On the Formulation of Deterministic Epidemic Models
All epidemic models are stochastic at the individual level. The adjective 'deterministic' just expresses that we focus on the limit of infinitely many individuals of all relevant categories. When we take a (caricatural) within-host model as the basis for a population level model, we obtain a structured model that can often be formulated in terms of delay equations (renewal equations, cf. Kermack-McKendrick 1927, and/or delay differential equations). The qualitative theory of such equations is in good shape, but there is an urgent need for numerical bifurcation tools.
09:30 to 10:00 H Heesterbeek (Universiteit Utrecht)
Modelling infectious agents in food webs
10:00 to 10:30 Morning Coffee
10:30 to 11:00 K Eames ([LSHTM])
Network measurement: past and future
We discuss common ways of collecting network data, and approaches that may be applied in the future; we cover the advantages and limitations of different methods, and note the difficulties inherent in defining a contact in a way that is easily understood, conveniently measured, and epidemiologically precise.
11:00 to 11:30 M Keeling (University of Warwick)
Future of network modelling

We discuss the latest progress and challenges in modelling infection spread through networks. We look to the future and suggest how these components could interact synergistically to provide a deeper understanding, as well as highlighting area where more fundamental research is required.

11:30 to 12:00 S Bansal (Georgetown University)
Network structure consequences and control: past and future
In this talk, we focus on the epidemiological consequences of network structure and the prospects for controlling them. We discuss insights that have been gleaned in the past on how network structure impacts disease dynamics and how this can be exploited for public health intervention design, and consider how these developments can be expanded in the future.
12:30 to 13:30 Lunch at Wolfson Court
13:30 to 14:00 T Bedford (University of Edinburgh)
What can we learn from viral phylogenies?
The coalescent was developed in the context of population genetics to infer population-level parameters from genetic data. It describes the effects of population size and demography on the genetic relationships among individuals in an evolving population. Here, I discuss how to relate the coalescent to inference of infectious disease dynamics. I cover mathematical theory, as well as statistical inference. I also discuss possibilities for future developments in joint inference using epidemiological and genetic data.
14:00 to 14:30 O Pybus
The Evolution & Adaptation of Influenza A Viruses in Swine
14:30 to 15:00 J Lloyd-Smith ([UCLA])
Whither disease ecology? Old problems and new solutions in a complex world
The study of disease dynamics in natural populations has made great strides in the last 20 years, but major challenges remain. Progress that has been made on single-host, single-pathogen systems must be extended to more complex natural communities, to address the dynamics of multiple pathogens circulating among multiple host species. Sometimes this boils down to classic problems, but often it reveals new dimensions that demand new empirical and theoretical approaches. In this talk, I will highlight some current challenges in multi-host systems, beginning with zoonotic pathogens as a relatively well-studied class of examples. I will discuss problems arising around cross-species 'spillover' transmission and subcritical 'stuttering' transmission, and how these processes influence our approach to classic questions such as the determinants of disease persistence. I will emphasize the interplay between models and data, and the challenges posed by epidemiologica l 'dark matter' (i.e. unobserved cases, or unobserved host species). To conclude, I will broaden the discussion to include ecological interactions among pathogen species, and the potential to study these using the (un-)natural experiments of pathogen introduction or eradication.
15:00 to 15:30 P Hudson (Pennsylvania State University)
Whither disease ecology? Old problems and new solutions
15:30 to 16:00 Afternoon Tea
16:00 to 16:30 S Bonhoeffer (ETH Zürich)
Recovering transmission structure and dynamics from viral sequence data
16:30 to 17:00 S Gupta (University of Oxford)
The role of multi-locus models in understanding within-host population dynamics
I will discuss how multi-locus models have helped us understand the dynamics of within-host antigenic variation with reference to Plasmodium falciparum and HIV.
Friday 23rd August 2013
09:00 to 09:30 B Williams ([SACEMA])
Ending AIDS: Past, Present and Yet to Come
Ending AIDS depends on the confluence of mathematics, epidemiology, public health and policy. Within ten years of the identification of the virus that leads to AIDS the key epidemiological parameters were well established. Within twenty years drugs were available to stop both disease progression and transmission. After thirty years the world still hesitates and argues about how best to proceed. We discuss what is known and what remains uncertain, areas in which more analytical work is needed, and consider briefly the politics of HIV.
09:30 to 10:00 A Ghani (Imperial College London)
Models for Malaria Control and Elimination
10:00 to 10:30 P Klepac (University of Cambridge)
International agreements for optimal disease control
One of the key issues in the control of immunizing infections is determining the optimal level of vaccination in a population and achieving it. What is optimal for a whole population might not be best for an individual; and what is optimal for one country might not be optimal for their neighbours. This talk describes how the optimum level of vaccination results from interplay between epidemiological dynamics and the economic constraints that shape and influence control strategies on local, national and international levels.

From an epidemiological perspective alone, vaccination policies are guided by the basic reproductive number R0 - the average number of new infections caused by a single case in a wholly susceptible population. In order to locally interrupt transmission, vaccination coverage should be at or above the critical elimination threshold, 1 - 1/R0. However, when local economic constraints in the form of the relative costs of vaccination and infection are added to this picture, the optimal control level can range anywhere from no intervention to elimination; for a non-virulent pathogen, it may be optimal to sustain immunization well below the elimination threshold.

Turning to consider multiple countries connected by migration, the incentives of one country to invest in vaccination are additionally dependent on their neighbours' vaccination coverage and infection status. In the absence of regional or global bodies that can impose a universal vaccination strategy, human mobility could promote free-riding on each others' vaccination efforts, leading to a below-optimal coverage (surprisingly, at a higher overall cost).

The last part of this talk outlines a potential solution to this problem, specifically the use of coalition formation as a regional public health tool. Theory suggests that self-enforcing coalitions can lead to higher, more consistent and more uniform regional vaccination coverage even in the absence of global enforcement, but how do they became a reality?

10:30 to 11:00 Morning Coffee
11:00 to 11:30 J Edmunds ([LSHTM])
Decision Making for Prevention/Control Under Economic Constraints
Twenty years ago Norman Bailey called for better co-ordination between mathematical modellers, public health officials and economists to improve public health decision-making. In this paper I review how well we have done in achieving this aim.
11:30 to 12:30 R Anderson (Imperial College London)
Recent progress in mathematical epidemiology and some future needs
The talk first briefly examine recent progress in mathematical epidemiology over the past decade with mention of: (1) inference - parameter estimation; (2) complex spatially structured stochastic models of transmission and control; (3) Visual display of results; (4) range of infectious disease addressed - both in Medicine and Veterinary sciences; and (5) influence in policy formulation - mathematical models now regarded by most as an essential tool in policy formulation.

The main part of the talk will focus on new research on the study of the transmission and control of the Neglected Tropical Diseases (NTDs), with emphasis on how models can help in the design of mass chemotherapy programmes.

12:30 to 13:30 Sandwich lunch at INI
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons