Simulation studies of St. Louis encephalitis and West Nile viruses: the impact of bird mortality

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.

Mechanistic models for West Nile virus transmission: a systematic review of features, aims and parametrization

Mathematical models within the Ross-Macdonald framework increasingly play a role in our understanding of vector-borne disease dynamics and as tools for assessing scenarios to respond to emerging threats. These threats are typically characterized by a high degree of heterogeneity, introducing a range of possible complexities in models and challenges to maintain the link with empirical evidence. We systematically identified and analysed a total of 77 published papers presenting compartmental West Nile virus (WNV) models that use parameter values derived from empirical studies. Using a set of 15 criteria, we measured the dissimilarity compared with the Ross-Macdonald framework. We also retrieved the purpose and type of models and traced the empirical sources of their parameters. Our review highlights the increasing refinements in WNV models. Models for prediction included the highest number of refinements. We found uneven distributions of refinements and of evidence for parameter values. We identified several challenges in parametrizing such increasingly complex models. For parameters common to most models, we also synthesize the empirical evidence for their values and ranges. The study highlights the potential to improve the quality of WNV models and their applicability for policy by establishing closer collaboration between mathematical modelling and empirical work.

Effects of Mosquito Biology on Modeled Chikungunya Virus Invasion Potential in Florida

Arboviruses transmitted by Aedes aegypti and Aedes albopictus have been introduced to Florida on many occasions. Infrequently, these introductions lead to sporadic local transmission and, more rarely, sustained local transmission. Both mosquito species are present in Florida, with spatio-temporal variation in population composition. We developed a two-vector compartmental, deterministic model to investigate factors influencing Chikungunya virus (CHIKV) establishment. The model includes a nonlinear, temperature-dependent mosquito mortality function based on minimum mortality in a central temperature region. Latin Hypercube sampling was used to generate parameter sets used to simulate transmission dynamics, following the introduction of one infected human. The analysis was repeated for three values of the mortality function central temperature. Mean annual temperature was consistently important in the likelihood of epidemics, and epidemics increased as the central temperature increased. Ae. albopictus recruitment was influential at the lowest central temperature while Ae. aegypti recruitment was influential at higher central temperatures. Our results indicate that the likelihood of CHIKV establishment may vary, but overall Florida is permissive for introductions. Model outcomes were sensitive to the specifics of mosquito mortality. Mosquito biology parameters are variable, and improved understanding of this variation will improve our ability to predict the outcome of introductions.

Predicting West Nile virus transmission in North American bird communities using phylogenetic mixed effects models and eBird citizen science data

BACKGROUND

West Nile virus (WNV) is a mosquito-transmitted disease of birds that has caused bird population declines and can spill over into human populations. Previous research has identified bird species that infect a large fraction of the total pool of infected mosquitoes and correlate with human infection risk; however, these analyses cover small spatial regions and cannot be used to predict transmission in bird communities in which these species are rare or absent. Here we present a mechanistic model for WNV transmission that predicts WNV spread (R0) in any bird community in North America by scaling up from the physiological responses of individual birds to transmission at the level of the community. We predict unmeasured bird species' responses to infection using phylogenetic imputation, based on these species' phylogenetic relationships with bird species with measured responses.

RESULTS

We focused our analysis on Texas, USA, because it is among the states with the highest total incidence of WNV in humans and is well sampled by birders in the eBird database. Spatio-temporal patterns: WNV transmission is primarily driven by temperature variation across time and space, and secondarily by bird community composition. In Texas, we predicted WNV R0 to be highest in the spring and fall when temperatures maximize the product of mosquito transmission and survival probabilities. In the most favorable months for WNV transmission (April, May, September and October), we predicted R0 to be highest in the "Piney Woods" and "Oak Woods & Prairies" ecoregions of Texas, and lowest in the "High Plains" and "South Texas Brush County" ecoregions. Dilution effect: More abundant bird species are more competent hosts for WNV, and predicted WNV R0 decreases with increasing species richness. Keystone species: We predicted that northern cardinals (Cardinalis cardinalis) are the most important hosts for amplifying WNV and that mourning doves (Zenaida macroura) are the most important sinks of infection across Texas.

CONCLUSIONS

Despite some data limitations, we demonstrate the power of phylogenetic imputation in predicting disease transmission in heterogeneous host communities. Our mechanistic modeling framework shows promise both for assisting future analyses on transmission and spillover in heterogeneous multispecies pathogen systems and for improving model transparency by clarifying assumptions, choices and shortcomings in complex ecological analyses.

Parasites of seabirds: A survey of effects and ecological implications

Parasites are ubiquitous in the environment, and can cause negative effects in their host species. Importantly, seabirds can be long-lived and cross multiple continents within a single annual cycle, thus their exposure to parasites may be greater than other taxa. With changing climatic conditions expected to influence parasite distribution and abundance, understanding current level of infection, transmission pathways and population-level impacts are integral aspects for predicting ecosystem changes, and how climate change will affect seabird species. In particular, a range of micro- and macro-parasites can affect seabird species, including ticks, mites, helminths, viruses and bacteria in gulls, terns, skimmers, skuas, auks and selected phalaropes (Charadriiformes), tropicbirds (Phaethontiformes), penguins (Sphenisciformes), tubenoses (Procellariiformes), cormorants, frigatebirds, boobies, gannets (Suliformes), and pelicans (Pelecaniformes) and marine seaducks and loons (Anseriformes and Gaviiformes). We found that the seabird orders of Charadriiformes and Procellariiformes were most represented in the parasite-seabird literature. While negative effects were reported in seabirds associated with all the parasite groups, most effects have been studied in adults with less information known about how parasites may affect chicks and fledglings. We found studies most often reported on negative effects in seabird hosts during the breeding season, although this is also the time when most seabird research occurs. Many studies report that external factors such as condition of the host, pollution, and environmental conditions can influence the effects of parasites, thus cumulative effects likely play a large role in how parasites influence seabirds at both the individual and population level. With an increased understanding of parasite-host dynamics it is clear that major environmental changes, often those associated with human activities, can directly or indirectly affect the distribution, abundance, or virulence of parasites and pathogens.

A two-thresholds policy to interrupt transmission of West Nile Virus to birds

This paper proposes a model of West Nile Virus (WNV) including threshold control policies concerning the culling of mosquitoes and birds under different conditions. Two thresholds are introduced to estimate whether and which control strategy should be implemented. For each mosquito threshold level [Formula: see text] the dynamical behaviour of the proposed non-smooth system is investigated as the bird threshold level [Formula: see text] varies, focusing on the existence of sliding domains, the existence of pseudo-equilibria, real or virtual of the endemic equilibria, global stability of these steady states, and the most interesting case of the occurrence of a novel globally asymptotically stable pseudo-attractor. The model solutions ultimately converge to a real equilibrium or a pseudo-equilibrium (if it exists), or a pseudo-attractor if no equilibrium is real and no pseudo-equilibrium exists. Here within, we show that the free system has a single stable endemic equilibrium under biologically reasonable assumptions, and show that when the control system has: (1) a bird-culling threshold that is above the bird equilibrium, culling has no advantage; (2) a bird-culling threshold that is below the bird equilibrium, but a mosquito-culling threshold that lies above the mosquito equilibrium, the infected bird population can be reduced but the infected mosquito population will remain the same; (3) a bird-culling threshold and a mosquito-culling threshold that both lie below their respective equilibrium values of the free system, then both the infected bird and mosquito populations can be reduced to lower levels. The results suggest that preset levels of the number of infected birds and infected mosquitoes can be maintained simultaneously when threshold values are chosen properly, which provides a possible control strategy when an emergent infectious disease cannot be eradicated immediately.

West Nile and St. Louis encephalitis viral genetic determinants of avian host competence

West Nile virus (WNV) and St. Louis encephalitis (SLEV) virus are enzootically maintained in North America in cycles involving the same mosquito vectors and similar avian hosts. However, these viruses exhibit dissimilar viremia and virulence phenotypes in birds: WNV is associated with high magnitude viremias that can result in mortality in certain species such as American crows (AMCRs, Corvus brachyrhynchos) whereas SLEV infection yields lower viremias that have not been associated with avian mortality. Cross-neutralization of these viruses in avian sera has been proposed to explain the reduced circulation of SLEV since the introduction of WNV in North America; however, in 2015, both viruses were the etiologic agents of concurrent human encephalitis outbreaks in Arizona, indicating the need to re-evaluate host factors and cross-neutralization responses as factors potentially affecting viral co-circulation. Reciprocal chimeric WNV and SLEV viruses were constructed by interchanging the pre-membrane (prM)-envelope (E) genes, and viruses subsequently generated were utilized herein for the inoculation of three different avian species: house sparrows (HOSPs; Passer domesticus), house finches (Haemorhous mexicanus) and AMCRs. Cross-protective immunity between parental and chimeric viruses were also assessed in HOSPs. Results indicated that the prM-E genes did not modulate avian replication or virulence differences between WNV and SLEV in any of the three avian species. However, WNV-prME proteins did dictate cross-protective immunity between these antigenically heterologous viruses. Our data provides further evidence of the important role that the WNV / SLEV viral non-structural genetic elements play in viral replication, avian host competence and virulence.

Since the identification of West Nile virus (WNV) in North America in 1999, St. Louis encephalitis virus (SLEV) cases declined rapidly. Both viruses utilize similar avian hosts and vectors for maintenance of transmission cycles; however, they present different phenotypes in both vector and avian host. In birds, WNV develops high viremias and elicits mortality whereas SLEV has not been associated with avian virulence. West Nile viral non-structural genetic elements have been demonstrated herein to dictate higher viremias in competent avian hosts and virulence in AMCRs. In contrast, non-structural SLEV elements previously have been shown to dictate increased oral infectivity in Culex mosquitoes, likely as a compensation for the lower viremias generated by SLEV. These findings coupled with the co-circulation of WNV and SLEV in Arizona in 2015 demonstrate that pre-existing flaviviral immunity does not necessarily preclude concurrent circulation of these viruses.

An Integrative Eco-Epidemiological Analysis of West Nile Virus Transmission

West Nile disease, caused by the West Nile virus (WNV), is a mosquito-borne zoonotic disease affecting humans and horses that involves wild birds as amplifying hosts. The mechanisms of WNV transmission remain unclear in Europe where the occurrence of outbreaks has dramatically increased in recent years. We used a dataset on the competence, distribution, abundance, diversity and dispersal of wild bird hosts and mosquito vectors to test alternative hypotheses concerning the transmission of WNV in Southern France. We modelled the successive processes of introduction, amplification, dispersal and spillover of WNV to incidental hosts based on host-vector contact rates on various land cover types and over four seasons. We evaluated the relative importance of the mechanisms tested using two independent serological datasets of WNV antibodies collected in wild birds and horses. We found that the same transmission processes (seasonal virus introduction by migratory birds, Culex modestus mosquitoes as amplifying vectors, heterogeneity in avian host competence, absence of 'dilution effect') best explain the spatial variations in WNV seroprevalence in the two serological datasets. Our results provide new insights on the pathways of WNV introduction, amplification and spillover and the contribution of bird and mosquito species to WNV transmission in Southern France.

Spatio-Temporal Distribution of Vector-Host Contact (VHC) Ratios and Ecological Niche Modeling of the West Nile Virus Mosquito Vector, Culex quinquefasciatus, in the City of New Orleans, LA, USA

The consistent sporadic transmission of West Nile Virus (WNV) in the city of New Orleans justifies the need for distribution risk maps highlighting human risk of mosquito bites. We modeled the influence of biophysical and socioeconomic metrics on the spatio-temporal distributions of presence/vector-host contact (VHC) ratios of WNV vector, Culex quinquefasciatus, within their flight range. Biophysical and socioeconomic data were extracted within 5-km buffer radii around sampling localities of gravid female Culex quinquefasciatus. The spatio-temporal correlations between VHC data and 33 variables, including climate, land use-land cover (LULC), socioeconomic, and land surface terrain were analyzed using stepwise linear regression models (RM). Using MaxEnt, we developed a distribution model using the correlated predicting variables. Only 12 factors showed significant correlations with spatial distribution of VHC ratios (R² = 81.62, p < 0.01). Non-forested wetland (NFWL), tree density (TD) and residential-urban (RU) settings demonstrated the strongest relationship. The VHC ratios showed monthly environmental resilience in terms of number and type of influential factors. The highest prediction power of RU and other urban and built up land (OUBL), was demonstrated during May-August. This association was positively correlated with the onset of the mosquito WNV infection rate during June. These findings were confirmed by the Jackknife analysis in MaxEnt and independently collected field validation points. The spatial and temporal correlations of VHC ratios and their response to the predicting variables are discussed.

Effects of rainfall on Culex mosquito population dynamics

The dynamics of a mosquito population depends heavily on climatic variables such as temperature and precipitation. Since climate change models predict that global warming will impact on the frequency and intensity of rainfall, it is important to understand how these variables affect the mosquito populations. We present a model of the dynamics of a Culex quinquefasciatus mosquito population that incorporates the effect of rainfall and use it to study the influence of the number of rainy days and the mean monthly precipitation on the maximum yearly abundance of mosquitoes M_max. Additionally, using a fracturing process, we investigate the influence of the variability in daily rainfall on M_max. We find that, given a constant value of monthly precipitation, there is an optimum number of rainy days for which M_max is a maximum. On the other hand, we show that increasing daily rainfall variability reduces the dependence of M_max on the number of rainy days, leading also to a higher abundance of mosquitoes for the case of low mean monthly precipitation. Finally, we explore the effect of the rainfall in the months preceding the wettest season, and we obtain that a regimen with high precipitations throughout the year and a higher variability tends to advance slightly the time at which the peak mosquito abundance occurs, but could significantly change the total mosquito abundance in a year.

Ecological niche modeling of mosquito vectors of West Nile virus in St. John's County, Florida, USA

Background

The lack of available vaccines and consistent sporadic transmission of WNV justify the need for mosquito vector control and prediction of their geographic distribution. However, the distribution of WNV transmission is dependent on the mosquito vector and the ecological requirements, which vary from one place to another.

Methods

Presence/density data of two WNV mosquito vectors, Culex nigripalpus and Cx. quinquefasciatus, was extracted within 5 km buffer zones around seropositive records of sentinel chickens in order to delineate their predicting variables and model the habitat suitability of probable infective mosquito using MaxEnt software. Different correlations between density data of the extracted mosquito vectors and 27 climate, land use-land cover, and land surface terrain variables were analyzed using linear regression analysis. Accordingly, the correlated predicting variables were used in building up habitat suitability model for the occurrence records of both mosquito vectors using MaxEnt.

Results

The density of both WNV mosquito vectors showed variation in their ecological requirements. Eight predicting variables, out of 27, had significant influence on density of Cx. nigripalpus. Precipitation of driest months was shown to be the best predicting variable for the density of this vector (R² = 41.70). Whereas, two variables were proven to predict the distribution of Cx. quinquefasciatus density. Vegetation showed the maximum predicting gain to the density of this mosquito vector (R² = 15.74), where nestling birds, in particular exotics, are found. Moreover, Jackknife analysis in MaxEnt demonstrated that urbanization and vegetation data layers significantly contribute in predicting habitat suitability of Cx. nigripalpus and Cx. quinquefasciatus occurrence, respectively, which justifies the contribution of the former in urban and the latter in epizootic transmission cycles of WNV. In addition, habitat suitability risk maps were produced for both vectors in response to their predicting variables.

Conclusions

For the first time in the study area, a quantitative relationship between 27 predicting variables and two WNV mosquito vectors within their foraging habitats was highlighted at the local scale. Accordingly, the predicting variables were used to produce a practical distribution map of probable infective mosquito vectors. This substantially helps in determining where suitable habitats are found. This will potentially help in designing target surveillance and control programmes, saving money, time and man-power. However, the suitability risk maps should be updated when serological and entomological data updates are available.

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.

A new model with delay for mosquito population dynamics

In this paper, we formulate a new model with maturation delay for mosquito population incorporating the impact of blood meal resource for mosquito reproduction. Our results suggest that except for the usual crowded effect for adult mosquitoes, the impact of blood meal resource in a given region determines the mosquito abundance, it is also important for the population dynamics of mosquito which may induce Hopf bifurcation. The existence of a stable periodic solution is proved both analytically and numerically. The new model for mosquito also suggests that the resources for mosquito reproduction should not be ignored or mixed with the impact of blood meal resources for mosquito survival and both impacts should be considered in the model of mosquito population. The impact of maturation delay is also analyzed.

Can Horton hear the whos? The importance of scale in mosquito-borne disease

The epidemiology of vector-borne pathogens is determined by mechanisms and interactions at different scales of biological organization, from individual-level cellular processes to community interactions between species and with the environment. Most research, however, focuses on one scale or level with little integration between scales or levels within scales. Understanding the interactions between levels and how they influence our perception of vector-borne pathogens is critical. Here two examples of biological scales (pathogen transmission and mosquito mortality) are presented to illustrate some of the issues of scale and to explore how processes on different levels may interact to influence mosquito-borne pathogen transmission cycles. Individual variation in survival, vector competence, and other traits affect population abundance, transmission potential, and community structure. Community structure affects interactions between individuals such as competition and predation, and thus influences the individual-level dynamics and transmission potential. Modeling is a valuable tool to assess interactions between scales and how processes at different levels can affect transmission dynamics. We expand an existing model to illustrate the types of studies needed, showing that individual-level variation in viral dose acquired or needed for infection can influence the number of infectious vectors. It is critical that interactions within and among biological scales and levels of biological organization are understood for greater understanding of pathogen transmission with the ultimate goal of improving control of vector-borne pathogens.

A transmission model for the ecology of an avian blood parasite in a temperate ecosystem

Most of our knowledge about avian haemosporidian parasites comes from the Hawaiian archipelago, where recently introduced Plasmodiumrelictum has contributed to the extinction of many endemic avian species. While the ecology of invasive malaria is reasonably understood, the ecology of endemic haemosporidian infection in mainland systems is poorly understood, even though it is the rule rather than the exception. We develop a mathematical model to explore and identify the ecological factors that most influence transmission of the common avian parasite, Leucocytozoonfringillinarum (Apicomplexa). The model was parameterized from White-crowned Sparrow (Zonotrichialeucophrys) and S. silvestre / craigi black fly populations breeding in an alpine ecosystem. We identify and examine the importance of altricial nestlings, the seasonal relapse of infected birds for parasite persistence across breeding seasons, and potential impacts of seasonal changes in black fly emergence on parasite prevalence in a high elevation temperate system. We also use the model to identify and estimate the parameters most influencing transmission dynamics. Our analysis found that relapse of adult birds and young of the year birds were crucial for parasite persistence across multiple seasons. However, distinguishing between nude nestlings and feathered young of the year was unnecessary. Finally, due to model sensitivity to many black fly parameters, parasite prevalence and sparrow recruitment may be most affected by seasonal changes in environmental temperature driving shifts in black fly emergence and gonotrophic cycles.

Effects of temperature on emergence and seasonality of West Nile virus in California

Temperature has played a critical role in the spatiotemporal dynamics of West Nile virus transmission throughout California from its introduction in 2003 through establishment by 2009. We compared two novel mechanistic measures of transmission risk, the temperature-dependent ratio of virus extrinsic incubation period to the mosquito gonotrophic period (BT), and the fundamental reproductive ratio (R(0)) based on a mathematical model, to analyze spatiotemporal patterns of receptivity to viral amplification. Maps of BT and R(0) were created at 20-km scale and compared throughout California to seroconversions in sentinel chicken flocks at half-month intervals. Overall, estimates of BT and R(0) agreed with intensity of transmission measured by the frequency of sentinel chicken seroconversions. Mechanistic measures such as these are important for understanding how temperature affects the spatiotemporal dynamics of West Nile virus transmission and for delineating risk estimates useful to inform vector control agency intervention decisions and communicate outbreak potential.

Multi-species interactions in West Nile virus infection

In this paper, we analyse the interaction of different species of birds and mosquitoes on the dynamics of West Nile virus (WNV) infection. We study the different transmission efficiencies of the vectors and birds and the impact on the possible outbreaks. We show that the basic reproductive number is the weighted mean of the basic reproductive number of each species, weighted by the relative abundance of its population in the location. These results suggest a possible explanation of why there are no outbreaks of WNV in Mexico.

The impact of maturation delay of mosquitoes on the transmission of West Nile virus

We formulate and analyze a delay differential equation model for the transmission of West Nile virus between vector mosquitoes and avian hosts that incorporates maturation delay for mosquitoes. The maturation time from eggs to adult mosquitoes is sensitive to weather conditions, in particular the temperature, and the model allows us to investigate the impact of this maturation time on transmission dynamics of the virus among mosquitoes and birds. Numerical results of the model show that a combination of the maturation time and the vertical transmission of the virus in mosquitoes has substantial influence on the abundance and number of infection peaks of the infectious mosquitoes.

The backward bifurcation in compartmental models for West Nile virus

In all of the West Nile virus (WNV) compartmental models in the literature, the basic reproduction number serves as a crucial control threshold for the eradication of the virus. However, our study suggests that backward bifurcation is a common property shared by the available compartmental models with a logistic type of growth for the population of host birds. There exists a subthreshold condition for the outbreak of the virus due to the existence of backward bifurcation. In this paper, we first review and give a comparison study of the four available compartmental models for the virus, and focus on the analysis of the model proposed by Cruz-Pacheco et al. to explore the backward bifurcation in the model. Our comparison study suggests that the mosquito population dynamics itself cannot explain the occurrence of the backward bifurcation, it is the higher mortality rate of the avian host due to the infection that determines the existence of backward bifurcation.

The Effect of Multiple Vectors on Arbovirus Transmission

Many mosquito-borne arboviruses have more than one competent vector. These vectors may or may not overlap in space and time, and may interact differently with vertebrate hosts. The presence of multiple vectors for a particular virus at one location over time will influence the epidemiology of the system, and could be important in the design of intervention strategies to protect particular hosts. A simulation model previously developed for West Nile and St. Louis encephalitis viruses and Culex nigripalpus was expanded to consider two vector species. These vectors differed in their abundance through the year, but were otherwise similar. The model was used to examine the consequences of different combinations of abundance patterns on the transmission dynamics of the virus. The abundance pattern based on Cx. nigripalpus dominated the system and was a key factor in generating epidemics in the wild bird population. The presence of two vectors often resulted in multiple epidemic peaks of transmission. A species which was active in the winter could enable virus persistence until another vector became active in the spring, summer, or fall. The day the virus was introduced into the system was critical in determining how many epidemic peaks were observed and when the first peak occurred. The number of epidemic peaks influenced the overall proportion of birds infected. The implications of these results for assessing the relative importance of different vector species are discussed.

Environmental risk factors associated with West Nile virus clinical disease in Florida horses

The objective of this study was to examine the extrinsic risk factors of West Nile virus (WNV) clinical disease in Florida horses as established from confirmed and negative horses tested within the state from 2001 to 2003. An Arboviral Case Information Form (ACF) was submitted by a referring veterinarian at the time of testing to the Florida Department of Agriculture and Consumer Services on every horse suspected of a viral encephalitis in Florida. A follow-up survey that focused on arbovirus prevention and farm ecology was created and mailed to the owner of each tested horse. Data from the follow-up survey indicated peak WNV prevalence in the late summer months in Florida. Quarter horses were the most commonly affected breed. The WNV vaccine was highly protective and natural water on the property also had a protective association. Factors that increased the risk of WNV to horses were the use of fans and a stable construction of solid wood or cement. Some risk indicators were dead birds on the property and other ill animals on the property. Data from this retrospective study have helped identify factors associated with WNV transmission in equines in Florida. Horses that have not been vaccinated and show clinical signs of arboviral infection from June to November should be tested for WNV. Horses that have been vaccinated and show clinical signs should be tested when the vaccination was administered within 1 month or greater than 6 months prior to the onset of clinical symptoms associated with WN infection.

Threshold conditions for west nile virus outbreaks

In this paper, we study the stability and saddle-node bifurcation of a model for the West Nile virus transmission dynamics. The existence and classification of the equilibria are presented. By the theory of K-competitive dynamical systems and index theory of dynamical systems on a surface, sufficient and necessary conditions for local stability of equilibria are obtained. We also study the saddle-node bifurcation of the system. Explicit subthreshold conditions in terms of parameters are obtained beyond the basic reproduction number which provides further guidelines for accessing control of the spread of the West Nile virus. Our results suggest that the basic reproductive number itself is not enough to describe whether West Nile virus will prevail or not and suggest that we should pay more attention to the initial state of West Nile virus. The results also partially explained the mechanism of the recurrence of the small scale endemic of the virus in North America.

Does reservoir host mortality enhance transmission of West Nile virus?

Background

Since its 1999 emergence in New York City, West Nile virus (WNV) has become the most important and widespread cause of mosquito-transmitted disease in North America. Its sweeping spread from the Atlantic to the Pacific coast was accompanied by widespread mortality among wild birds, especially corvids. Only sporadic avian mortality had previously been associated with this infection in the Old World. Here, we examine the possibility that reservoir host mortality may intensify transmission, both by concentrating vector mosquitoes on remaining hosts and by preventing the accumulation of "herd immunity".

Results

Inspection of the Ross-Macdonald expression of the basic reproductive number (R₀) suggests that this quantity may increase with reservoir host mortality. Computer simulation confirms this finding and indicates that the level of virulence is positively associated with the numbers of infectious mosquitoes by the end of the epizootic. The presence of reservoir incompetent hosts in even moderate numbers largely eliminated the transmission-enhancing effect of host mortality. Local host die-off may prevent mosquitoes to "waste" infectious blood meals on immune host and may thus facilitate perpetuation and spread of transmission.

Conclusion

Under certain conditions, host mortality may enhance transmission of WNV and similarly maintained arboviruses and thus facilitate their emergence and spread. The validity of the assumptions upon which this argument is built need to be empirically examined.

Modeling and biological control of mosquitoes

Models can be useful at many different levels when considering complex issues such as biological control of mosquitoes. At an early stage, exploratory models are valuable in exploring the characteristics of an ideal biological control agent and for guidance in data collection. When more data are available, models can be used to explore alternative control strategies and the likelihood of success. There are few modeling studies that explicitly consider biological control in mosquitoes; however, there have been many theoretical studies of biological control in other insect systems and of mosquitoes and mosquito-borne diseases in general. Examples are used here to illustrate important aspects of designing, using and interpreting models. The stability properties of a model are valuable in assessing the potential of a biological control agent, but may not be relevant to a mosquito population with frequent environmental perturbations. The time scale and goal of proposed control strategies are important considerations when analyzing a model. The underlying biology of the mosquito host and the biological control agent must be carefully considered when deciding what to include in a model. Factors such as density dependent population growth in the host, the searching efficiency and aggregation of a natural enemy, and the resource base of both have been shown to influence the stability and dynamics of the interaction. Including existing mosquito control practices into a model is useful if biological control is proposed for locations with current insecticidal control. The development of Integrated Pest Management (IPM) strategies can be enhanced using modeling techniques, as a wide variety of options can be simulated and examined. Models can also be valuable in comparing alternate routes of disease transmission and to investigate the level of control needed to reduce transmission.

Eradicating vector-borne diseases via age-structured culling

We derive appropriate mathematical models to assess the effectiveness of culling as a tool to eradicate vector-borne diseases. The model, focused on the culling strategies determined by the stages during the development of the vector, becomes either a system of autonomous delay differential equations with impulses (in the case where the adult vector is subject to culling) or a system of nonautonomous delay differential equations where the time-varying coefficients are determined by the culling times and rates (in the case where only the immature vector is subject to culling). Sufficient conditions are derived to ensure eradication of the disease, and simulations are provided to compare the effectiveness of larvicides and insecticide sprays for the control of West Nile virus. We show that eradication of vector-borne diseases is possible by culling the vector at either the immature or the mature phase, even though the size of the vector is oscillating and above a certain level.

Transmission assumptions generate conflicting predictions in host-vector disease models: a case study in West Nile virus

This review synthesizes the conflicting outbreak predictions generated by different biological assumptions in host-vector disease models. It is motivated by the North American outbreak of West Nile virus, an emerging infectious disease that has prompted at least five dynamical modelling studies. Mathematical models have long proven successful in investigating the dynamics and control of infectious disease systems. The underlying assumptions in these epidemiological models determine their mathematical structure, and therefore influence their predictions. A crucial assumption is the host-vector interaction encapsulated in the disease-transmission term, and a key prediction is the basic reproduction number, R(0). We connect these two model elements by demonstrating how the choice of transmission term qualitatively and quantitatively alters R(0) and therefore alters predicted disease dynamics and control implications. Whereas some transmission terms predict that reducing the host population will reduce disease outbreaks, others predict that this will exacerbate infection risk. These conflicting predictions are reconciled by understanding that different transmission terms apply biologically only at certain population densities, outside which they can generate erroneous predictions. For West Nile virus, R(0) estimates for six common North American bird species indicate that all would be effective outbreak hosts.

A comparison of continuous and discrete-time West Nile virus models

The first recorded North American epidemic of West Nile virus was detected in New York state in 1999, and since then the virus has spread and become established in much of North America. Mathematical models for this vector-transmitted disease with cross-infection between mosquitoes and birds have recently been formulated with the aim of predicting disease dynamics and evaluating possible control methods. We consider discrete and continuous time versions of the West Nile virus models proposed by Wonham et al. [Proc. R. Soc. Lond. B 271:501-507, 2004] and by Thomas and Urena [Math. Comput. Modell. 34:771-781, 2001], and evaluate the basic reproduction number as the spectral radius of the next-generation matrix in each case. The assumptions on mosquito-feeding efficiency are crucial for the basic reproduction number calculation. Differing assumptions lead to the conclusion from one model [Wonham, M.J. et al., [Proc. R. Soc. Lond. B] 271:501-507, 2004] that a reduction in bird density would exacerbate the epidemic, while the other model [Thomas, D.M., Urena, B., Math. Comput. Modell. 34:771-781, 2001] predicts the opposite: a reduction in bird density would help control the epidemic.

A dynamic transmission model of eastern equine encephalitis virus

Eastern equine encephalitis virus (EEEV) is one of several arthropod-borne viruses (arboviruses) endemic to the United States. Interactions between arthropod (mosquito) vectors and avian amplification host populations play a significant role in the dynamics of arboviral transmission. Recent data have suggested the hypothesis that an increased rate of successful feeding on young-of-the-year (YOY) birds might play a role in the dynamics of EEEV transmission. To test this hypothesis, we developed a model to explore the effect of the interactions of the vectors and avian host populations on EEEV transmission. Sensitivity analyses conducted using this model revealed eleven parameters that were capable of disproportionately affecting the predicted level of EEEV infection in the vertebrate reservoir and vector populations. Of these, four parameters were related to the interaction of the vector with young-of-the-year birds. Furthermore, adult birds could not substitute for young-of-the-year in initiating and maintaining a predicted enzootic outbreak of EEEV. Taken together, the model predicted that young-of-the-year birds play a key role in establishing and maintaining enzootic outbreaks of EEEV.

Ecological mechanisms that promote arbovirus survival: a mathematical model of Ross River virus transmission

Many assessments of host and vector competence for arboviruses focus on level and length of infectivity and ignore ecological mechanisms that contribute to virus survival. In this paper, mathematical models are used to compare local survival mechanisms for a range of scenarios, using Ross River virus as a case study. Ross River virus is an Australian arbovirus with many mosquito vectors and reservoir hosts. The mechanisms for maintaining long-term transmission of the virus vary between salt and freshwater mosquito vectors, and according to the availability of susceptible hosts. The models demonstrate that overwintering of virus in adult freshwater mosquitoes requires a large host population, while overwintering of virus in infected eggs of saltwater mosquitoes is an effective survival strategy when filial infection rates are high. The virus survives longer when both salt and freshwater mosquito species are included in the model than when only one mosquito species is present. When the marsupial host is replaced by a host with higher birth rate and shorter infectious period, the virus survived longer under all models. This suggests that birth rate can be a key factor when assessing the competence of reservoir hosts to maintain virus transmission.

An epidemiological model for West Nile virus: invasion analysis and control applications

Infectious diseases present ecological and public health challenges that can be addressed with mathematical models. Certain pathogens, however, including the emerging West Nile virus (WN) in North America, exhibit a complex seasonal ecology that is not readily analysed with standard epidemiological methods. We develop a single-season susceptible-infectious-removed (SIR) model of WN cross-infection between birds and mosquitoes, incorporating specific features unique to WN ecology. We obtain the disease reproduction number, R0, and show that mosquito control decreases, but bird control increases, the chance of an outbreak. We provide a simple new analytical and graphical method for determining, from standard public health indicators, necessary mosquito control levels. We extend this method to a seasonally variable mosquito population and outline a multi-year model framework. The model's numerical simulations predict disease levels that are consistent with independent data.

Simulation studies of St. Louis encephalitis virus in south Florida

Two simulation models were used to investigate the epidemiology of St. Louis encephalitis virus (SLEv) in south Florida, one including sentinel hosts (chickens) and amplification hosts (wild birds), while the other one included age structure in the amplification host population. The overall population size of the vector, Culex nigripalpus, was a major factor in the likelihood of epizootics for both models, but the seasonal dynamics of the vector alone did not explain variation in transmission. Interactions between seasonal factors in the mosquito and reproduction in the wild amplification avian hosts appeared to be important in the likelihood of epizootics. Biased feeding between sentinel and amplification hosts affected the time course of virus prevalence and may have implications for the interpretation of sentinel data. The time of virus introduction strongly affected the timing of outbreaks but did not affect the likelihood of epizootics. In most cases, the outbreak occurred immediately after virus introduction; however, in some cases the outbreak was delayed until the mosquito population increased. This has implications for the timing of control strategies directed against mosquito populations.