Spatial heterogeneity in ecological models : two case studies

Two models are developed to explore the dynamics associated with spatial heterogeneity. The first model is the expansion of a single cell, fish population model to a landscape of interacting cells. The second model is a tick-borne disease model using a set of differential equations applied to a series of spatial patches. The spatially-explicit landscape fish population model (ALFISH) is a part of the Across Trophic Level System Simulation (ATLSS) project for the freshwater wetlands of the Everglades and Big Cypress Swamp. ALFISH was applied as part of the ATLSS project to Everglades restoration, one of the largest ecological restoration projects in the world. ALFISH has been improved to include new field information as that information became available. The only variable input into ALFISH is the hydrology. Up to 35% of variation in fish populations observed in field data corresponds to the variations predicted by ALFISH. The differential equations underlying the tick-borne disease model designed for the lone star tick (Amblyomma americanum) are analytically evaluated for one patch. The results show that under given criteria for the parameters, the system would be locally stable. For further study, the system is then solved numerically. Patches are identified as either grass or wooded and connected by migration. The disease is endemic in both patches unless some type of control is applied. If a control is applied, the disease is reduced to extremely low levels. If two patches, one grass and one wooded, are linked by migration, applying the control to the wooded patch is effective for controlling the disease while applying it in the grass patch is not. A final simulation using a twelve patch system is run to create results to compare with field data. The results show that the model produced qualitatively similar results to the field data which give reductions of 60% in tick density in the areas with control applied

Modelling the Effects of Habitat and Hosts on Tick Invasions

Many tick species are invading new areas because of anthropogenic changes in the landscape, shifting climatic variables and increasing populations of suitable host species and tick habitat. However, the relative influences of habitat and hosts in tick dispersal and tick population establishment remain in question. A spatially explicit agent-based model was developed to explore the spatio-temporal dynamics of a generic tick population in the years immediately following the introduction of ticks into a novel environment. The general model was then adapted to investigate a case study of two recent tick species invasions into the Mid-Atlantic United States. The recent simultaneous range expansions of two ixodid tick species, Ixodes affinis and Amblyomma maculatum, provided an opportunity to determine if invasion patterns observed in the field could be replicated in silico on a small scale. The models presented here indicated that for generalist parasites, habitat connectivity is a better indicator than host mobility for spatial and genetic patterns of parasite range expansion. In addition, our results demonstrate the utility of including genetic variables into agent-based models: gene flow functions as a proxy for measuring dispersal, and models can be validated using results from the field

Rift Valley Fever: An Economic Assessment of Agricultural and Human Vulnerability

This research focused on the assessment of the U.S. agricultural sector and human vulnerability to a Rift Valley Fever (RVF) outbreak and the implications of a select set of alternative disease control strategies. Livestock impact assessment is done by using an integrated epidemic/economic model to examine the extent of RVF spread in the Southeast Texas livestock population and its consequences plus the outcome of implementing two different control strategies: emergency vaccination and larvicide vector control separately plus when they are used simultaneously. Human impact assessment utilized an inferential procedure, which comprises of a cost of illness calculation to assess the dollar cost of human illnesses and deaths, as well as a Disability Adjusted Life Year calculation to give an estimate of the burden of disease on public health as a whole. Results indicate substantial potential losses to the U.S., where combined livestock and human national costs ranged from $121 million to$2.3 billion.Rift Valley Fever, Outbreak, Welfare, Vaccination, Larvicide., Environmental Economics and Policy, Food Consumption/Nutrition/Food Safety, Food Security and Poverty, Health Economics and Policy,

Use of Optimal Control Models to Predict Treatment Time for Managing Tick-Borne Disease

Tick-borne diseases have been on the rise recently, and correspondingly, there is an increased interest in implementing control measures to decrease the risk. Optimal control provides an ideal tool to identify the best method for reducing risk while accounting for the associated costs. Using a previously published model, a variety of frameworks are assessed to identify the key factors influencing mitigation strategies. The level and duration of tick-reducing efforts are key metrics for understanding the successful reduction in tick-borne disease incidence. The results show that the punctuated nature of the tick\u27s life history plays a critical role in reducing risk without the need for a permanent treatment programme. This work suggests that across a variety of optimal control frameworks and objective functionals within a closed environment, similar strategies are created, all suggesting that the tick-borne disease risk can be reduced to near zero without completely eliminating the tick population

Use of LYMESIM 2.0 to assess the potential for single and integrated management methods to control blacklegged ticks (Ixodes scapularis; Acari: Ixodidae) and transmission of Lyme disease spirochetes

Annual Lyme disease cases continue to rise in the U.S. making it the most reported vector-borne illness in the country. The pathogen (Borrelia burgdorferi) and primary vector (Ixodes scapularis; blacklegged tick) dynamics of Lyme disease are complicated by the multitude of vertebrate hosts and varying environmental factors, making models an ideal tool for exploring disease dynamics in a time- and cost-effective way. In the current study, LYMESIM 2.0, a mechanistic model, was used to explore the effectiveness of three commonly used tick control methods: habitat-targeted acaricide (spraying), rodent-targeted acaricide (bait boxes), and white-tailed deer targeted acaricide (4-poster devices). Work was done to evaluate their effectiveness when used alone and in combination with one another. Optimized application strategies were also identified. Additionally, pilot work was done to incorporate prescribed fire into the model and compare its efficacy to the acaricide-based approaches. It was determined that any singular use or combination of methods that included spraying were most effective amongst acaricide-based treatments, suppressing the density of I. scapularisnymphs (DON) by \u3e80%. Furthermore, the best time to apply treatments was between January and mid-April, and mid-September to early December. Optimized treatment strategies identified by the model include application of treatment twice annually, every other year at a minimum effectiveness of 25%, which achieves 80% DON suppression and no increases in I. scapularis nymphs once treatments are complete. Interestingly, preliminary work to integrate prescribed fire in the model indicated that it achieved 93-100% efficacy in burn years and one-year post burn, making prescribed fire more effective than all acaricide-based treatments. Overall, this study illustrates the value in using models to identify the best method of blacklegged tick population control that is both time- and cost-effective. Future field research should be done to validate the findings of this model

Prevalence of Ehrlichia chaffeensis and Ehrlichia ewingii in Amblyomma americanum and Dermacentor variabilis Collected From Southeastern Virginia, 2010-2011

Amblyomma americanum is the most commonly-encountered tick species in southeastern Virginia, representing approximately 95% of the human-biting tick population in this area. Here we investigated the prevalence of Ehrlichia chaffeensis and Ehrlichia ewingii in questing Amblyomma americanum and Dermacentor variabilis ticks collected from multiple sites in southeastern Virginia from 2010–2011. Although both Ehrlichia species were detected in Amblyomma americanum, no evidence of either pathogen was found in Dermacentor variabilis. Prevalence of E. chaffeensis varied by location, ranging from 0 – 5.08% among Amblyomma americanum populations. Ehrlichia ewingii prevalence was slightly higher, ranging from 0 – 8.20% among A. americanum populations. We conclude that both pathogens are established in southeastern Virginia A. americanum populations, and that although there are no apparent temporal trends in Ehrlichia prevalence, there is variation among locations, suggesting the potential for disease hotspots

Multipatch Stochastic Epidemic Model for the Dynamics of a Tick-Borne Disease

Spatial heterogeneity and migration of hosts and ticks have an impact on the spread, extinction and persistence of tick-borne diseases. In this paper, we investigate the impact of between-patch migration of white-tailed deer and lone star ticks on the dynamics of a tick-borne disease with regard to disease extinction and persistence using a system of Itô stochastic differential equations model. It is shown that the disease-free equilibrium exists and is unique. The general formula for computing the basic reproduction number for all patches is derived. We show that for patches in isolation, the basic reproduction number is equal to the largest patch reproduction number and for connected patches it lies between the minimum and maximum of the patch reproduction numbers. Numerical simulations for a two-patch deterministic and stochastic differential equation models are performed to illustrate the dynamics of the disease for varying migration rates. Our results show that the probability of eliminating or minimizing the disease in both patches is high when there is no migration unlike when it is present. The results imply that the probability of disease extinction can be increased if deer and tick movement are controlled or even prohibited especially when there is an outbreak in one or both patches since movement can introduce a disease in an area that was initially disease-free. Thus, screening of infectives in protected areas such as deer farms, private game parks or reserves, etc. before they migrate to other areas can be one of the intervention strategies for controlling and preventing disease spread

Scoping Review of Distribution Models for Selected \u3ci\u3eAmblyomma\u3c/i\u3e Ticks and Rickettsial Group Pathogens

The rising prevalence of tick-borne diseases in humans in recent decades has called attention to the need for more information on geographic risk for public health planning. Species distribution models (SDMs) are an increasingly utilized method of constructing potential geographic ranges. There are many knowledge gaps in our understanding of risk of exposure to tick-borne pathogens, particularly for those in the rickettsial group. Here, we conducted a systematic scoping review of the SDM literature for rickettsial pathogens and tick vectors in the genus Amblyomma. Of the 174 reviewed articles, only 24 studies used SDMs to estimate the potential extent of vector and/or pathogen ranges. The majority of studies (79%) estimated only tick distributions using vector presence as a proxy for pathogen exposure. Studies were conducted at different scales and across multiple continents. Few studies undertook original data collection, and SDMs were mostly built with presence-only datasets from public database or surveillance sources. The reliance on existing data sources, using ticks as a proxy for disease risk, may simply reflect a lag in new data acquisition and a thorough understanding of the tick-pathogen ecology involved

“Beyond BIO2010: Celebration and Opportunities” at the Intersection of Mathematics and Biology

With this special edition of CBE-LSE, which focuses on connections between and integration of the biological and mathematical sciences, it is especially fitting that we report on an important symposium, Beyond BIO2010: Celebration and Opportunities,1 which was held at the National Acad- emy of Sciences (NAS) in Washington, D.C. on May 21–22, 2010. This symposium was organized to assess what progress has been made in addressing the challenges and recommendations in the National Research Council’s (NRC) report: BIO2010: Transforming Undergraduate Education for Future Research Biologists (NRC, 2003a). Most of the presen- tations and posters at this event emphasized the increasing connections of the life and mathematical sciences in under- graduate education. The symposium was initiated by the U.S. National Committee to the International Union of Bio- logical Sciences and was hosted by the National Academies’ Board on Life Sciences.

Newer Surveillance Data Extends Our Understanding of the Niche of \u3ci\u3eRickettsia montanensis\u3c/i\u3e (Rickettsiales: Rickettsiaceae) Infection of the American Dog Tick (Acari: Ixodidae) in the United States

Background: Understanding the geographic distribution of Rickettsia montanensis infections in Dermacentor variabilis is important for tick-borne disease management in the United States, as both a tick-borne agent of interest and a potential confounder in surveillance of other rickettsial diseases. Two previous studies modeled niche suitability for D. variabilis with and without R. montanensis, from 2002-2012, indicating that the D. variabilis niche overestimates the infected niche. This study updates these, adding data since 2012. Methods: Newer surveillance and testing data were used to update Species Distribution Models (SDMs) of D. variabilis, and R. montanensis infected D. variabilis, in the United States. Using random forest (RF) models, found to perform best in previous work, we updated the SDMs and compared them with prior results. Warren’s I niche overlap metric was used to compare between predicted suitability for all ticks and ‘pathogen positive niche’ models across datasets. Results: Warren’s I indicated \u3c 2% change in predicted niche, and there was no change in order of importance of environmental predictors, for D. variabilis or R. montanensis positive niche. The updated D. variabilis niche model overpredicted suitability compared to the updated R. montanensis positive niche in key peripheral parts of the range, but slightly underpredicted through the northern and midwestern parts of the range. This reinforces previous findings of a more constrained pathogen-positive niche than predicted by D. variabilis records alone. Conclusions: The consistency of predicted niche suitability for D. variabilis in the United States, with the addition of nearly a decade of new data, corroborates this is a species with generalist habitat requirements. Yet a slight shift in updated niche distribution, even of low suitability, included more southern areas, pointing to a need for continued and extended monitoring and surveillance. This further underscores the importance of revisiting vector and vector-borne disease distribution maps