A hierarchical network approach for modeling Rift Valley fever epidemics with applications in North America

Rift Valley fever is a vector-borne zoonotic disease which causes high morbidity and mortality in livestock. In the event Rift Valley fever virus is introduced to the United States or other non-endemic areas, understanding the potential patterns of spread and the areas at risk based on disease vectors and hosts will be vital for developing mitigation strategies. Presented here is a general network-based mathematical model of Rift Valley fever. Given a lack of empirical data on disease vector species and their vector competence, this discrete time epidemic model uses stochastic parameters following several PERT distributions to model the dynamic interactions between hosts and likely North American mosquito vectors in dispersed geographic areas. Spatial effects and climate factors are also addressed in the model. The model is applied to a large directed asymmetric network of 3,621 nodes based on actual farms to examine a hypothetical introduction to some counties of Texas, an important ranching area in the United States of America (U.S.A.). The nodes of the networks represent livestock farms, livestock markets, and feedlots, and the links represent cattle movements and mosquito diffusion between different nodes. Cattle and mosquito (Aedes and Culex) populations are treated with different contact networks to assess virus propagation. Rift Valley fever virus spread is assessed under various initial infection conditions (infected mosquito eggs, adults or cattle). A surprising trend is fewer initial infectious organisms result in a longer delay before a larger and more prolonged outbreak. The delay is likely caused by a lack of herd immunity while the infections expands geographically before becoming an epidemic involving many dispersed farms and animals almost simultaneously

Does reservoir host mortality enhance transmission of West Nile virus?

<p>Abstract</p> <p>Background</p> <p>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".</p> <p>Results</p> <p>Inspection of the Ross-Macdonald expression of the basic reproductive number (<it>R</it>₀) 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.</p> <p>Conclusion</p> <p>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.</p

Man Bites Mosquito: Understanding the Contribution of Human Movement to Vector-Borne Disease Dynamics

In metropolitan areas people travel frequently and extensively but often in highly structured commuting patterns. We investigate the role of this type of human movement in the epidemiology of vector-borne pathogens such as dengue. Analysis is based on a metapopulation model where mobile humans connect static mosquito subpopulations. We find that, due to frequency dependent biting, infection incidence in the human and mosquito populations is almost independent of the duration of contact. If the mosquito population is not uniformly distributed between patches the transmission potential of the pathogen at the metapopulation level, as summarized by the basic reproductive number, is determined by the size of the largest subpopulation and reduced by stronger connectivity. Global extinction of the pathogen is less likely when increased human movement enhances the rescue effect but, in contrast to classical theory, it is not minimized at an intermediate level of connectivity. We conclude that hubs and reservoirs of infection can be places people visit frequently but briefly and the relative importance of human and mosquito populations in maintaining the pathogen depends on the distribution of the mosquito population and the variability in human travel patterns. These results offer an insight in to the paradoxical observation of resurgent urban vector-borne disease despite increased investment in vector control and suggest that successful public health intervention may require a dual approach. Prospective studies can be used to identify areas with large mosquito populations that are also visited by a large fraction of the human population. Retrospective studies can be used to map recent movements of infected people, pinpointing the mosquito subpopulation from which they acquired the infection and others to which they may have transmitted it

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

A Spatial Model of Mosquito Host-Seeking Behavior

Mosquito host-seeking behavior and heterogeneity in host distribution are important factors in predicting the transmission dynamics of mosquito-borne infections such as dengue fever, malaria, chikungunya, and West Nile virus. We develop and analyze a new mathematical model to describe the effect of spatial heterogeneity on the contact rate between mosquito vectors and hosts. The model includes odor plumes generated by spatially distributed hosts, wind velocity, and mosquito behavior based on both the prevailing wind and the odor plume. On a spatial scale of meters and a time scale of minutes, we compare the effectiveness of different plume-finding and plume-tracking strategies that mosquitoes could use to locate a host. The results show that two different models of chemotaxis are capable of producing comparable results given appropriate parameter choices and that host finding is optimized by a strategy of flying across the wind until the odor plume is intercepted. We also assess the impact of changing the level of host aggregation on mosquito host-finding success near the end of the host-seeking flight. When clusters of hosts are more tightly associated on smaller patches, the odor plume is narrower and the biting rate per host is decreased. For two host groups of unequal number but equal spatial density, the biting rate per host is lower in the group with more individuals, indicative of an attack abatement effect of host aggregation. We discuss how this approach could assist parameter choices in compartmental models that do not explicitly model the spatial arrangement of individuals and how the model could address larger spatial scales and other probability models for mosquito behavior, such as Lévy distributions

Avian Host-Selection by Culex pipiens in Experimental Trials

Evidence from field studies suggests that Culex pipiens, the primary mosquito vector of West Nile virus (WNV) in the northeastern and north central United States, feeds preferentially on American robins (Turdus migratorius). To determine the contribution of innate preferences to observed preference patterns in the field, we conducted host preference trials with a known number of adult female C. pipiens in outdoor cages comparing the relative attractiveness of American robins with two common sympatric bird species, European starling, Sternus vulgaris and house sparrow, Passer domesticus. Host seeking C. pipiens were three times more likely to enter robin-baited traps when with the alternate host was a European starling (n = 4 trials; OR = 3.06; CI [1.42–6.46]) and almost twice more likely when the alternative was a house sparrow (n = 8 trials; OR = 1.80; CI = [1.22–2.90]). There was no difference in the probability of trap entry when two robins were offered (n = 8 trials). Logistic regression analysis determined that the age, sex and weight of the birds, the date of the trial, starting-time, temperature, humidity, wind-speed and age of the mosquitoes had no effect on the probability of a choosing a robin over an alternate bird. Findings indicate that preferential feeding by C. pipiens mosquitoes on certain avian hosts is likely to be inherent, and we discuss the implications innate host preferences may have on enzootic WNV transmission

A Simple Stochastic Model with Environmental Transmission Explains Multi-Year Periodicity in Outbreaks of Avian Flu

Avian influenza virus reveals persistent and recurrent outbreaks in North American wild waterfowl, and exhibits major outbreaks at 2–8 years intervals in duck populations. The standard susceptible-infected- recovered (SIR) framework, which includes seasonal migration and reproduction, but lacks environmental transmission, is unable to reproduce the multi-periodic patterns of avian influenza epidemics. In this paper, we argue that a fully stochastic theory based on environmental transmission provides a simple, plausible explanation for the phenomenon of multi-year periodic outbreaks of avian flu. Our theory predicts complex fluctuations with a dominant period of 2 to 8 years which essentially depends on the intensity of environmental transmission. A wavelet analysis of the observed data supports this prediction. Furthermore, using master equations and van Kampen system-size expansion techniques, we provide an analytical expression for the spectrum of stochastic fluctuations, revealing how the outbreak period varies with the environmental transmission

Does Global Warming Increase Establishment Rates of Invasive Alien Species? A Centurial Time Series Analysis

BACKGROUND: The establishment rate of invasive alien insect species has been increasing worldwide during the past century. This trend has been widely attributed to increased rates of international trade and associated species introductions, but rarely linked to environmental change. To better understand and manage the bioinvasion process, it is crucial to understand the relationship between global warming and establishment rate of invasive alien species, especially for poikilothermic invaders such as insects. METHODOLOGY/PRINCIPAL FINDINGS: We present data that demonstrate a significant positive relationship between the change in average annual surface air temperature and the establishment rate of invasive alien insects in mainland China during 1900-2005. This relationship was modeled by regression analysis, and indicated that a 1 °C increase in average annual surface temperature in mainland China was associated with an increase in the establishment rate of invasive alien insects of about 0.5 species year⁻¹. The relationship between rising surface air temperature and increasing establishment rate remained significant even after accounting for increases in international trade during the period 1950-2005. Moreover, similar relationships were detected using additional data from the United Kingdom and the contiguous United States. CONCLUSIONS/SIGNIFICANCE: These findings suggest that the perceived increase in establishments of invasive alien insects can be explained only in part by an increase in introduction rate or propagule pressure. Besides increasing propagule pressure, global warming is another driver that could favor worldwide bioinvasions. Our study highlights the need to consider global warming when designing strategies and policies to deal with bioinvasions