Seminars (IDD)

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.

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.

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.

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.

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.

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: •https://statnet.csde.washington.edu/trac - the statnet wiki •http://www.jstatsoft.org/v24/ - Journal of Statistical Software Volume on statnet (2008) •http://statnet.csde.washington.edu/movies/ - A network epidemiology movie

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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?

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.