A stochastic multi-host model for West Nile virus transmission.

When initially introduced into a susceptible population, a disease may die out or result in a major outbreak. We present a Continuous-Time Markov Chain model for enzootic WNV transmission between two avian host species and a single vector, and use multitype branching process theory to determine the probability of disease extinction based upon the type of infected individual initially introducing the disease into the population - an exposed vector, infectious vector, or infectious host of either species. We explore how the likelihood of disease extinction depends on the ability of each host species to transmit WNV, vector biting rates on host species, and the relative abundance of host species, as well as vector abundance. Theoretical predictions are compared to the outcome of stochastic simulations. We find the community composition of hosts and vectors, as well as the means of disease introduction, can greatly affect the probability of disease extinction.

Implicit versus explicit vector management strategies in models for vector-borne disease epidemiology.

Throughout the vector-borne disease modeling literature, there exist two general frameworks for incorporating vector management strategies (e.g. area-wide adulticide spraying and larval source reduction campaigns) into vector population models, namely, the "implicit" and "explicit" control frameworks. The more simplistic "implicit" framework facilitates derivation of mathematically rigorous results on disease suppression and optimal control, but the biological connection of these results to real-world "explicit" control actions that could guide specific management actions is vague at best. Here, we formally define a biological and mathematical relationship between implicit and explicit control, and we provide mathematical expressions relating the strength of implicit control to management-relevant properties of explicit control for four common intervention strategies. These expressions allow the optimal control and basic reproduction number analyses typically utilized in implicit control modeling to be interpreted directly in terms of real-world actions and real-world monetary costs. Our methods reveal that only certain sub-classes of explicit control protocols are able to be represented as implicit controls, and that implicit control is a meaningful approximation of explicit control only when resonance-like synergistic effects between multiple explicit controls have negligible effects on population reduction. When non-negligible synergy exists, implicit control results, despite their mathematical tidiness, fail to provide accurate predictions regarding vector control and disease spread. Collectively, these elements build an effective bridge between analytically interesting and mathematically tractable implicit control and the challenging, action-oriented explicit control.

Managing disease outbreaks: The importance of vector mobility and spatially heterogeneous control.

Management strategies for control of vector-borne diseases, for example Zika or dengue, include using larvicide and/or adulticide, either through large-scale application by truck or plane or through door-to-door efforts that require obtaining permission to access private property and spray yards. The efficacy of the latter strategy is highly dependent on the compliance of local residents. Here we develop a model for vector-borne disease transmission between mosquitoes and humans in a neighborhood setting, considering a network of houses connected via nearest-neighbor mosquito movement. We incorporate large-scale application of adulticide via aerial spraying through a uniform increase in vector death rates in all sites, and door-to-door application of larval source reduction and adulticide through a decrease in vector emergence rates and an increase in vector death rates in compliant sites only, where control efficacies are directly connected to real-world experimentally measurable control parameters, application frequencies, and control costs. To develop mechanistic insight into the influence of vector motion and compliance clustering on disease controllability, we determine the basic reproduction number R0 for the system, provide analytic results for the extreme cases of no mosquito movement, infinite hopping rates, and utilize degenerate perturbation theory for the case of slow but non-zero hopping rates. We then determine the application frequencies required for each strategy (alone and combined) in order to reduce R0 to unity, along with the associated costs. Cost-optimal strategies are found to depend strongly on mosquito hopping rates, levels of door-to-door compliance, and spatial clustering of compliant houses, and can include aerial spray alone, door-to-door treatment alone, or a combination of both. The optimization scheme developed here provides a flexible tool for disease management planners which translates modeling results into actionable control advice adaptable to system-specific details.

Temporal and Spatial Impacts of Hurricane Damage on West Nile Virus Transmission and Human Risk.

Hurricanes have profound impacts on zoonotic pathogen ecosystems that exhibit spatial and temporal waves in both distance from and time since the event. Wind, rain, and storm surge directly affect mosquito vectors and animal hosts of these pathogens. In this analysis, we apply a West Nile virus transmission model parameterized for the Northern coast of the Gulf of Mexico to explore the effect of event timing of hurricane landfall, time since the event, and damage extent on human West Nile virus neuro-invasive disease (WNV-NID) risk. Early-season hurricanes, which make landfall prior to the peak of baseline WNV transmission activity, increase the average total WNV-infectious mosquitoes for the year by 7.8% and human WNV-NID incidence by 94.3% across all areas with hurricane damage. The indirect effects on human exposure to mosquito bites in the immediate aftermath and long-term recovery from the event have strong impacts on the risk of infection. The resultant interactive direct and indirect storm effects on the pathogen system are spatially and temporally heterogenous among the generalized time and space categories modeled.

Comparative proteomic analysis between nitrogen supplemented and starved conditions in Magnaporthe oryzae.

BACKGROUND: Fungi are constantly exposed to nitrogen limiting environments, and thus the efficient regulation of nitrogen metabolism is essential for their survival, growth, development and pathogenicity. To understand how the rice blast pathogen Magnaporthe oryzae copes with limited nitrogen availability, a global proteome analysis under nitrogen supplemented and nitrogen starved conditions was completed. METHODS: M. oryzae strain 70-15 was cultivated in liquid minimal media and transferred to media with nitrate or without a nitrogen source. Proteins were isolated and subjected to unfractionated gel-free based liquid chromatography-tandem mass spectrometry (LC-MS/MS). The subcellular localization and function of the identified proteins were predicted using bioinformatics tools. RESULTS: A total of 5498 M. oryzae proteins were identified. Comparative analysis of protein expression showed 363 proteins and 266 proteins significantly induced or uniquely expressed under nitrogen starved or nitrogen supplemented conditions, respectively. A functional analysis of differentially expressed proteins revealed that during nitrogen starvation nitrogen catabolite repression, melanin biosynthesis, protein degradation and protein translation pathways underwent extensive alterations. In addition, nitrogen starvation induced accumulation of various extracellular proteins including small extracellular proteins consistent with observations of a link between nitrogen starvation and the development of pathogenicity in M. oryzae. CONCLUSION: The results from this study provide a comprehensive understanding of fungal responses to nitrogen availability.

A host stage-structured model of enzootic West Nile virus transmission to explore the effect of avian stage-dependent exposure to vectors.

Though seasonal West Nile virus (WNV) outbreaks have been widely observed to be associated with the end of the avian nesting season, specific ecological mechanisms accounting for this synchronicity remain poorly understood. In this paper we develop and evaluate a novel mathematical model of enzootic WNV transmission to gain insight into the mechanisms responsible for structuring WNV dynamics. We incorporate avian (host) stage-structure (nestling, fledgling, and adult) and within-species heterogeneity in the form of stage-specific mosquito (vector) biting rates. We determine the extent to which temporal fluctuations in host stage and vector abundance throughout the season, along with the differential exposure of these stages to mosquito bites, affect the timing and magnitude of WNV outbreaks in the vector population. We find heterogeneity in avian stage exposure, particularly an increase in juvenile exposure, to result in earlier, more intense transmission. The effects of differential exposure are dependent upon vector abundance, both at carrying capacity as well as during initial stages of nestling production.

Analysis of a waterborne disease model with socioeconomic classes.

Waterborne diseases such as cholera continue to pose serious public health problems in the world today. Transmission parameters can vary greatly with socioeconomic class (SEC) and the availability of clean water. We formulate a multi-patch waterborne disease model such that each patch represents a particular SEC with its own water source, allowing individuals to move between SECs. For a 2-SEC model, we investigate the conditions under which each SEC is responsible for driving a cholera outbreak. We determine the effect of SECs on disease transmission dynamics by comparing the basic reproduction number of the 2-SEC model to that of a homogeneous model that does not take SECs into account. We conclude by extending several results of the 2-SEC model to an n-SEC model.

Heterogeneity in multiple transmission pathways: modelling the spread of cholera and other waterborne disease in networks with a common water source.

Many factors influencing disease transmission vary throughout and across populations. For diseases spread through multiple transmission pathways, sources of variation may affect each transmission pathway differently. In this paper we consider a disease that can be spread via direct and indirect transmission, such as the waterborne disease cholera. Specifically, we consider a system of multiple patches with direct transmission occurring entirely within patch and indirect transmission via a single shared water source. We investigate the effect of heterogeneity in dual transmission pathways on the spread of the disease. We first present a 2-patch model for which we examine the effect of variation in each pathway separately and propose a measure of heterogeneity that incorporates both transmission mechanisms and is predictive of R(0). We also explore how heterogeneity affects the final outbreak size and the efficacy of intervention measures. We conclude by extending several results to a more general n-patch setting.

Identifiability and estimation of multiple transmission pathways in cholera and waterborne disease.

Cholera and many waterborne diseases exhibit multiple characteristic timescales or pathways of infection, which can be modeled as direct and indirect transmission. A major public health issue for waterborne diseases involves understanding the modes of transmission in order to improve control and prevention strategies. An important epidemiological question is: given data for an outbreak, can we determine the role and relative importance of direct vs. environmental/waterborne routes of transmission? We examine whether parameters for a differential equation model of waterborne disease transmission dynamics can be identified, both in the ideal setting of noise-free data (structural identifiability) and in the more realistic setting in the presence of noise (practical identifiability). We used a differential algebra approach together with several numerical approaches, with a particular emphasis on identifiability of the transmission rates. To examine these issues in a practical public health context, we apply the model to a recent cholera outbreak in Angola (2006). Our results show that the model parameters-including both water and person-to-person transmission routes-are globally structurally identifiable, although they become unidentifiable when the environmental transmission timescale is fast. Even for water dynamics within the identifiable range, when noisy data are considered, only a combination of the water transmission parameters can practically be estimated. This makes the waterborne transmission parameters difficult to estimate, leading to inaccurate estimates of important epidemiological parameters such as the basic reproduction number (R0). However, measurements of pathogen persistence time in environmental water sources or measurements of pathogen concentration in the water can improve model identifiability and allow for more accurate estimation of waterborne transmission pathway parameters as well as R0. Parameter estimates for the Angola outbreak suggest that both transmission pathways are needed to explain the observed cholera dynamics. These results highlight the importance of incorporating environmental data when examining waterborne disease.

Life stages: interactions and spatial patterns.

In many stage-structured species, different life stages often occupy separate spatial niches in a heterogeneous environment. Life stages of the giant flour beetle Tribolium brevicornis (Leconte), in particular adults and pupae, occupy different locations in a homogeneous habitat. This unique spatial pattern does not occur in the well-studied stored grain pests T. castaneum (Herbst) and T. confusum (Duval). We propose density dependent dispersal as a causal mechanism for this spatial pattern. We model and explore the spatial dynamics of T. brevicornis with a set of four density dependent integrodifference and difference equations. The spatial model exhibits multiple attractors: a spatially uniform attractor and a patchy attractor with pupae and adults spatially separated. The model attractors are consistent with experimental observations.