Decelerating Spread of West Nile Virus by Percolation in a Heterogeneous Urban Landscape

Vector-borne diseases are emerging and re-emerging in urban environments throughout the world, presenting an increasing challenge to human health and a major obstacle to development. Currently, more than half of the global population is concentrated in urban environments, which are highly heterogeneous in the extent, degree, and distribution of environmental modifications. Because the prevalence of vector-borne pathogens is so closely coupled to the ecologies of vector and host species, this heterogeneity has the potential to significantly alter the dynamical systems through which pathogens propagate, and also thereby affect the epidemiological patterns of disease at multiple spatial scales. One such pattern is the speed of spread. Whereas standard models hold that pathogens spread as waves with constant or increasing speed, we hypothesized that heterogeneity in urban environments would cause decelerating travelling waves in incipient epidemics. To test this hypothesis, we analysed data on the spread of West Nile virus (WNV) in New York City (NYC), the 1999 epicentre of the North American pandemic, during annual epizootics from 2000–2008. These data show evidence of deceleration in all years studied, consistent with our hypothesis. To further explain these patterns, we developed a spatial model for vector-borne disease transmission in a heterogeneous environment. An emergent property of this model is that deceleration occurs only in the vicinity of a critical point. Geostatistical analysis suggests that NYC may be on the edge of this criticality. Together, these analyses provide the first evidence for the endogenous generation of decelerating travelling waves in an emerging infectious disease. Since the reported deceleration results from the heterogeneity of the environment through which the pathogen percolates, our findings suggest that targeting control at key sites could efficiently prevent pathogen spread to remote susceptible areas or even halt epidemics

Rapid simulation of spatial epidemics : a spectral method

Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or sub-populations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended ‘image’ of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational efficiency of spatial simulations. We demonstrate the efficiency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel

Rapid simulation of spatial epidemics : a spectral method

Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or sub-populations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended ‘image’ of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational efficiency of spatial simulations. We demonstrate the efficiency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel

Human mobility and spatial disease dynamics

The understanding of human mobility and the development of qualitative models as well as quantitative theories for it is of key importance to the research of human infectious disease dynamics on large geographical scales. In our globalized world, mobility and traffic have reached a complexity and volume of unprecedented degree. Long range human mobility is now responsible for the rapid geographical spread of emergent infectious diseases. Multiscale human mobility networks exhibit two prominent features: (1) Networks exhibit a strong heterogeneity, the distribution of weights, traffic fluxes and populations sizes of communities range over many orders of magnitude. (2) Although the interaction magnitude in terms of traffic intensities decreases with distance, the observed power-laws indicate that long range interactions play a significant role in spatial disease dynamics. We will review how the topological features of traffic networks can be incorporated in models for disease dynamics and show, that the way topology is translated into dynamics can have a profound impact on the overall disease dynamics. We will also introduce a class of spatially extended models in which the impact and interplay of both spatial heterogeneity as well as long range spatial interactions can be investigated in a systematic fashion. Our analysis of multiscale human mobility networks is based on a proxy network of dispersing US dollar bills, which we incorporated in a model to produce real-time epidemic forecasts that projected the spatial spread of the recent outbreak of Influenza A(H1N1)

Recurrent host mobility in spatial epidemics: beyond reaction-diffusion

Human mobility is a key factor in spatial disease dynamics and related phenomena. In computational models host mobility is typically modelled by diffusion in space or on metapolulation networks. Alternatively, an effective force of infection across distance has been introduced to capture spatial dispersal implicitly. Both approaches do not account for important aspects of natural human mobility, diffusion does not capture the high degree of predictability in natural human mobility patters, e.g. the high percentage of return movements to individuals' base location, the effective force of infection approach assumes immediate equilibrium with respect to dispersal. These conditions are typically not met in natural scenarios. We investigate an epidemiological model that explicitly captures natural individual mobility patterns. We systematically investigate generic dynamical features of the model on regular lattices as well as metapopulation networks and show that generally the model exhibits significant dynamical differences in comparison to ordinary diffusion and effective force of infection models. For instance, the natural human mobility model exhibits a saturation of wave front speeds and a novel type of invasion threshold that is a function of the return rate in mobility patterns. In the light of these new findings and with the availability of precise and pervasive data on human mobility our approach provides a framework for a more sophisticated modeling of spatial disease dynamics

Modelling the multi-scaled nature of pest outbreaks

Recent research suggests that the spread of pest outbreaks is driven by ecological processes acting at different spatial scales. In this work, we establish a network model for the analysis and management of pest outbreaks that takes into account small-scale host-pest interactions as well as landscape topology and connectivity. The model explains outbreak cycles both for geometrid moths and bark beetles, and provides insight into the relative importance and interactions between the multi-scale drivers of outbreak dynamics. Our results demonstrate that outbreak behavior is most sensitive to changes in pest pressure at the local scale, and that accounting for the spatial connectivity of habitat patches is crucial to capturing the spreading behavior through landscapes. In contrast to early warning signals based on retrospective data, our model provides predictions of future outbreak risk based on a mechanistic understanding of the system, which we apply for landscape-scale forest management

Elucidating the phylodynamics of endemic rabies virus in eastern Africa using whole-genome sequencing

Many of the pathogens perceived to pose the greatest risk to humans are viral zoonoses, responsible for a range of emerging and endemic infectious diseases. Phylogeography is a useful tool to understand the processes that give rise to spatial patterns and drive dynamics in virus populations. Increasingly, whole-genome information is being used to uncover these patterns, but the limits of phylogenetic resolution that can be achieved with this are unclear. Here, whole-genome variation was used to uncover fine-scale population structure in endemic canine rabies virus circulating in Tanzania. This is the first whole-genome population study of rabies virus and the first comprehensive phylogenetic analysis of rabies virus in East Africa, providing important insights into rabies transmission in an endemic system. In addition, sub-continental scale patterns of population structure were identified using partial gene data and used to determine population structure at larger spatial scales in Africa. While rabies virus has a defined spatial structure at large scales, increasingly frequent levels of admixture were observed at regional and local levels. Discrete phylogeographic analysis revealed long-distance dispersal within Tanzania, which could be attributed to human-mediated movement, and we found evidence of multiple persistent, co-circulating lineages at a very local scale in a single district, despite on-going mass dog vaccination campaigns. This may reflect the wider endemic circulation of these lineages over several decades alongside increased admixture due to human-mediated introductions. These data indicate that successful rabies control in Tanzania could be established at a national level, since most dispersal appears to be restricted within the confines of country borders but some coordination with neighbouring countries may be required to limit transboundary movements. Evidence of complex patterns of rabies circulation within Tanzania necessitates the use of whole-genome sequencing to delineate finer scale population structure that can that can guide interventions, such as the spatial scale and design of dog vaccination campaigns and dog movement controls to achieve and maintain freedom from disease

Stochastic spatial models of plant diseases

I present three models of plant--pathogen interactions. The models are stochastic and spatially explicit at the scale of individual plants. For each model, I use a version of pair approximation or moment closure along with a separation of timescales argument to determine the effects of spatial clustering on threshold structure. By computing the spatial structure early in an invasion, I find explicit corrections to mean field theory. In the first chapter, I present a lattice model of a disease that is not directly lethal to its host, but affects its ability to compete with neighbors. I use a type of pair approximation to determine conditions for invasions and coexistence. In the second chapter, I study a basic SIR epidemic point process in continuous space. I implement a multiplicative moment closure scheme to compute the threshold transmission rate as a function of spatial parameters. In the final chapter, I model the evolution of pathogen resistance when two plant species share a pathogen. Evolution may lead to non--resistance by a host that finds the disease to be a useful weapon. I use a lattice model with the ordinary pair approximation assumption to study phenotypic evolution via repeated invasions by novel strains.Comment: Ph.D. Dissertation; 140 pages; 75 EPS figures; Latex2

Epidemic Models as Scaling Limits of Individual Dynamics

Infection spread among individuals is modelled with a continuous time Markov chain, in which subject interactions depend on their distance in space. The well known SIR model and non local variants of the latter are then obtained as large scale limits of the individual based model in two different scaling regimes of the interaction.Comment: 22 page