MBI Videos

Workshop 4: Evolution and Spread of Disease

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    Nicole Mideo
    Parasite evolution is increasingly being recognized as one of the most important challenges in applied evolutionary biology. Understanding how parasites maximize fitness whilst facing the diverse challenges of living in cells, hosts, and vectors, is central to disease control and offers a novel testing ground for evolutionary theory. Along with Sam Brown, I recently hosted a symposium to address the question "How do parasites maximise fitness across a range of biological scales?". The symposium brought together researchers whose work looks across scales and environments to understand why and how parasites 'do what they do', tying together mechanism, evolutionary explanations, and public health implications. I will report on some of the fascinating research that suggests that understanding the evolution of parasite traits � and the diseases they cause � often requires an appreciation that parasite lives are complex and forces outwith focal host-parasite interactions can shape their traits. I will also highlight an existing theoretical framework for studying parasite evolution, which should provide a useful starting point for embracing this complexity.
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    Alessandro Vespignani
    Mathematical and computational models are increasingly used in support decisions in public health, however the perception of their reliability and the criteria for their uses is contrasted among domain experts. We consider the Global Epidemic and Mobility model that generates stochastic realizations of epidemic evolution worldwide from which we can gather information such as prevalence, morbidity, number of secondary cases and number and date of imported cases for 3,360 subpopulation in 220 countries with a time resolution of 1 day. GLEaM has been used to anticipate the geographical spreading for the 2009 H1N1 pandemic by estimating the transmission potential and the relevant model parameters with a Monte Carlo likelihood analysis of the arrival time distribution generated by 1 million computationally simulated epidemics. We present an extensive validation analysis of the obtained results from surveillance and virological sources collected in 46 countries of the Northern Hemisphere during the course of the pandemic. We focus on discussing the challenges posed by the real-time estimation of parameters, the different levels of data-integration and the validation through high quality data sets. In particular, data gathered during and after the 2009 H1N1 influenza crisis represent an unprecedented opportunity to i) test the robustness of the prediction intervals with respect to additional parameters unknown concurrently or before the end of the pandemic; ii) test the sensitivity of prediction intervals to the different levels of data integration by considering progressively increasing knowledge of socio-demographic and human mobility data.
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    Frank Ball
    The basic reproduction number R0 is one of the most important quantities in epidemiology. However, for epidemic models with explicit social structure involving small mixing units such as households, its definition is not straightforward and a wealth of other threshold parameters has appeared in the literature. In this talk I use branching processes to define R0, apply this definition to models with households or other more complex social structures, provide a method for calculating R0 and show inequalities comparing R0 with previous threshold parameters. The comparisons imply that, if R0 > 1, vaccinating a fraction 1 - 1/R0 of the population, chosen uniformly at random, with a perfect vaccine is insufficient to be sure of preventing a large outbreak, and they lead to sharper, easily-computed bounds for the critical vaccination coverage than were previously available.

    Based on work done jointly with Lorenzo Pellis (Imperial College London) and Pieter Trapman (Stockholm University).
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    Tom Britton
    In the talk we present a simple extension of the configuration model to weighted networks, and state some asymptotic properties of the network model. The weights may be used for some stochastic process taking place on the network; for example an epidemic where the probability of transmission between two individuals depends on the weight of the connected edge (the weight for example reflecting social distance). We also consider the case where individuals (nodes) are heterogeneous in he sense that the transmission probability depends on the infectivity of the infector and the susceptibility of the victim. We end with analysis of some empirical networks: movement of patients in hospitals in Stockholm (for mrsa), workplaces and households of the Swedish population (for influenza), and census of sex-contacts (for STDs).
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    Jean-Stephane Dhersin
    We consider a SIR epidemic model propagating on a random network generated by a configuration model, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemics is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles. These three degree distributions are sufficient to describe the course of the disease. The limit in large population is investigated. As a corollary, this provides a rigorous proof of equations obtained by Volz.

    This is a joint work with Laurent Decreusefond, Pascal Moyal and Viet Chi Tran
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    Viet Chi Tran
    HIV has been introduced in Cuban in 1986. From the beginning of the epidemics, contact-tracing is used, in the purpose of detecting more HIV-positive individuals and of controlling the spread of the disease. The data generated from this contact-tracing program provide some partial information on the social networks underlying the propagation of HIV. In this talk, we present this big network (5389 nodes, with a giant component of 2386 nodes) together with some possible modelling of the phenomenon.
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    Philip O'Neill
    Multi-drug resistant pathogens such as MRSA and VRE give rise to substantial morbidity and mortality, and impose a huge economic burden on healthcare systems. In this talk we describe a framework for analysing patient-level data from hosptials on such pathogens, employing stochastic transmission models and using Markov chain Monte Carlo methods witin a Bayesian statistical framework. The methods are illustrated with various data sets and used to address various clinically-relevant questions.
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    Jose Ponciano Castellanos
    Our understanding of the ecological and evolutionary conditions that permit the establishment and persistence of different bacterial species in host-associated microbial communities is incomplete. Recent work done to characterize human vaginal bacterial communities by experimental and analytical approaches has shown that idiosyncratic changes in species composition and wide fluctuations in the relative abundances of the different species are undeniably associated with specific environmental drivers. An understanding of the mechanisms, ecological processes and evolutionary routes behind the genesis of such associations and fluctuations remain an important knowledge gap. If the structure and composition of a given ecological community often alternates between distinct, widely different states, then better predictions about the chances of a dramatic community shift can be achieved using mechanistic, stochastic population dynamics models. In human bacterial communities research, there is a strong need to confront problems of risk assessment and prediction using such modeling approach. In this work, we develop a modeling framework based on the multivariate Ornstein-Uhlenbeck stochastic process to predict the unfolding of complex microbial community dynamics. We derive a suite of stochastic models derived from first biological principles will be used to evaluate time-series data on the relative abundances of bacterial species in vaginal communities. The statistical inferences done with these models have broad implications to the understanding of the processes governing the composition, structure and function of bacterial communities associated to humans. Finally, our research opens the door to a better assessment of the risk to diseases associated with responses to disturbances of human-associated microbial ecosystems.
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    Shweta Bansal
    In models of disease transmission on contact networks, the probability of exposure is determined by the connectivity (degree) of the individual (node). Thus, the most highly connected individuals in a contact network have both a higher probability of spreading infection through the population and a higher rate of exposure (susceptibility) through social contacts. As an epidemic sweeps through a population, this heterogeneity leads to systematic structural changes in the active portion of the network, removing immunized individuals who no longer participate in the chains of transmission. While the impact of network structure on the progression of an epidemic has been well studied, there has been relatively little work on network evolution during the course of an epidemic. We analytically investigate the impact of epidemic dynamics on the underlying host population structure and find that the structural evolution of the network varies with the original topology of the network and the contagiousness of the disease. We identify the mechanisms acting on the network topology to make them sparser, consider questions about the patterns of immunity that arise during disease outbreaks, and explore their impact on future epidemics and key public health policies.
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    Johan Metz
    Models for the evolution of virulence traditionally assume a trade-off between inverse disease-induced mortality rate and infectivity, resulting in intermediate virulence. The underlying intuition is that faster growing agent populations do both more damage and produce more infective particles. This intuition implicitly assumes a well-mixed host body. In reality both damage and infectivity depend mainly on the location in the body where the agents lodge. This is related i.a. to the surface proteins that allow agents to dock on and penetrate into different cell types. The typical example is respiratory diseases where more deeply seated ones are both less infective and more harmful. With the other standard assumption, full cross-immunity between disease strains, this would lead to evolution towards the tip of the nose. In reality cross-immunity depends on surface antigens and hence is at least in part connected to depth. In this talk I discuss a simple adaptive dynamics style model taking on board the aforementioned considerations. The inference is that disease diversity should decrease with depth.

    (The reported work was done in collaboration with Kevin Kleine and Juan E. Keymer Vergara of Delft University of Technology.)
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    Jan Medlock
    Virulence evolution has a long history, including the now-classic paper of Gandon et al. 2001 on the impact of malaria vaccination on the virulence of the parasite. Gandon et al. found that a vaccine with the action of reducing the pathogen growth rate in the host selects for more virulent pathogens, while an infection-blocking vaccine selects for less virulent pathogens. We found that, in the context of mosquito transgenesis, that relaxing one assumption of Gandon et al. leads to an inability to predict the direction of selection on pathogen virulence. I will discuss these issues in the context of dengue vaccine.
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    Ayalvadi Ganesh
    Tuberculosis is one of the major global diseases in terms of both prevalance and mortality. In recent decades, strains of the disease have evolved that are resistant to several, or all, of the drugs used to treat the disease. Drug resistance is conferred by rare mutations, raising the question of how multiple mutations might have arisen in a single strain. Motivated by this question, we study models of branching processes with mutations which generalize the pioneering work of Luria and Delbruck. We look at the sizes of mutant populations in the limit of mutation rates decreasing to zero, and characterize their limiting distribution. The results show a transition between two regimes depending on the relative growth rate of the mutants: in the slow growth regime, the limiting distribution is Gaussian, while if the mutants reproduce quickly enough, it is heavy-tailed.
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    Nicolas Champagnat
    We consider an stochastic, individual-based model of an evolving population with logistic density-dependence, where individuals are characterized by a quantitative phenotypic trait. Under appropriate parameters scalings of rare mutations and large populations, we obtain a stochastic jump process on the mutation time-scale, where evolution proceeds through successive invasions of mutants, followed by competition phases on shorter time scales, where disadvantaged traits are eliminated. Under an additional scaling of small mutations and on an appropriate time scales, the evolution can be described as ordinary differential equations on the trait space, known as "canonical equations of adaptive dynamics", followed by diversification phases where the number of traits present in the population may increase, a phenomenon known as "evolutionary branching".

    This is joint work with Sylvie M�l�ard (Ecole Polytechnique).

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