Infectious disease modeling and the dynamics of transmission.

The dynamics of any infectious disease are heavily dependent on the rate of transmission from infectious to susceptible hosts. In many disease models, this rate is captured in a single compound parameter, the probability of transmission P. However, closer examination reveals how beta can be further decomposed into a number of biologically relevant variables, including contact rates among individuals and the probability that contact events actually result in disease transmission. We start by introducing some of the basic concepts underlying the different approaches to modeling disease transmission and by laying out why a more detailed understanding of the variables involved is usually desirable. We then describe how parameter estimates of these variables can be derived from empirical data, drawing primarily from the existing literature on human diseases. Finally, we discuss how these concepts and approaches may be applied to the study of pathogen transmission in wildlife diseases. In particular, we highlight recent technical innovations that could help to overcome some the logistical challenges commonly associated with empirical disease research in wild populations.

Animal-based national surveillance for zoonotic disease: quality, limitations, and implications of a model system for monitoring rabies.

Surveillance for zoonotic diseases among wildlife is a research and public health challenge. The inherent limitations posed by the requisite human-animal interactions are often undefined and underappreciated. The national surveillance system for animal rabies in the United States was examined as a model system; reporting of animal rabies is legally mandated, each case of rabies is laboratory confirmed, and data have been consistently collected for more than 50 years. Factors influencing the monthly counts of animal rabies tests reported during 1992-2001 were assessed by univariate and multivariable regression methods. The suitability of passively collected surveillance data for determining the presence or absence of the raccoon-associated variant of rabies within states and within individual counties was assessed by determining critical threshold values from the regression analyses. The size of the human population and total expenditures within a county accounted for 72% and 67%, respectively, of the variance in testing. The annual median number of rabies tests performed was seven for counties without rabies, 22 for counties with non-raccoon rabies, and 34 for counties with raccoon rabies. Active surveillance may be required in locales with sparse human populations when a high degree of confidence in the status of rabies is required.

Assessing the role of long-distance translocation and spatial heterogeneity in the raccoon rabies epidemic in Connecticut.

Spatial heterogeneity and long-distance translocation (LDT) play important roles in the spatio-temporal dynamics and management of emerging infectious diseases and invasive species. We assessed the influence of LDT events on the invasive spread of raccoon rabies through Connecticut. We identified several putative LDT events, and developed a network-model to evaluate whether they became new foci for epidemic spread. LDT was fairly common, but many of the LDTs were isolated events that did not spread. Two putative LDT events did appear to become nascent foci that affected the epidemic in surrounding townships. In evaluating the role of LDT, we simultaneously revisited the problem of spatial heterogeneity. The spread of raccoon rabies is associated with forest cover--rabies moves up to three-times slower through the most heavily forested townships compared with those with less forestation. Forestation also modified the effect of rivers. In the best overall model, rabies did not cross the river separating townships that were heavily forested, and the spread slowed substantially between townships that were lightly forested. Our results suggest that spatial heterogeneity can be used to enhance the effects of rabies control by focusing vaccine bait distribution along rivers in lightly forested areas. LDT events are a concern, but this analysis suggests that at a local scale they can be isolated and managed.

Persistence of elevated rabies prevention costs following post-epizootic declines in rates of rabies among raccoons (Procyon lotor).

Determining the benefits to cost relationships among different approaches to rabies control and prevention has been hindered by the inherent temporal variability in the dynamics of disease among wildlife reservoir hosts and a tangible and objective measure of the cost of rabies prevention. A major and unavoidable component of rabies prevention programs involves diagnostic testing of animals and the subsequent initiation of appropriate public health responses. The unit cost per negative and positive diagnostic test outcome can be reasonably estimated. This metric when linked to methodologies subdividing the epizootic process into distinct temporal stages provided the requisite detail to estimate benefits derived from rabies control strategies. Oral rabies vaccine (ORV), for prevention of the raccoon-associated variant of rabies, has been distributed in Ohio and adjoining states in an effort to develop an immune barrier to the westward spread of epizootic raccoon rabies. The costs of ORV delivery have been quantified. Herein, the cost structures required to assess the benefits accrued by prevention were developed. A regression model was developed effectively predicting (r2=0.70) the total number of rabies diagnostic tests performed by 53 counties in five northeastern (NE) states from 1992 to 2001. Five temporal stages sufficed to capture the range of variability in the raccoon rabies epizootic process. Unit costs, dollars per diagnostic test outcome, were calculated for negative and positive results from published reports. Ohio counties were matched to NE counties based on similar socioeconomic characters. A "pseudo-epizootic" of raccoon rabies was introduced into Ohio and the costs savings from ORV were derived as the excess costs imposed by epizootic spread throughout the state. At 46 km/year (range modeled, 30-60 km/year), the pseudo epizootic spread, and reached the enzootic stage, in all Ohio counties by year 13 (range modeled, 11-17 years). Cumulative excess costs for Ohio ranged between $11 and $21 million; counties of low socioeconomic status experienced the greatest relative excess costs. The costs for rabies prevention activities reached apices during the epizootic stage of raccoon rabies (2.7-10.8 times baseline) an unforeseen finding indicated elevated costs persisted (1.7-7.2 times baseline) into the enzootic stage.

Spatial dynamics and molecular ecology of North American rabies.

Rabies, caused by a single-stranded RNA virus, is arguably the most important viral zoonotic disease worldwide. Although endemic throughout many regions for millennia, rabies is also undergoing epidemic expansion, often quite rapid, among wildlife populations across regions of Europe and North America. A current rabies epizootic in North America is largely attributable to the accidental introduction of a particularly well-adapted virus variant into a naive raccoon population along the Virginia/West Virginia border in the mid-1970s. We have used the extant database on the spatial and temporal occurrence of rabid raccoons across the eastern United States to construct predictive models of disease spread and have tied patterns of emergence to local environmental variables, genetic heterogeneity, and host specificity. Rabies will continue to be a remarkable model system for exploring basic issues in the temporal and spatial dynamics of expanding infectious diseases and examining ties between disease population ecology and evolutionary genetics at both micro- and macro-evolutionary time scales.

Temporal dynamics of rabies in a wildlife host and the risk of cross-species transmission.

An epidemiological model was developed for rabies, linking the risk of disease in a secondary species (cats) to the temporal dynamics of disease in a wildlife reservoir (raccoons). Data were obtained from cats, raccoons, and skunks tested for rabies in the northeastern United States during 1992-2000. An epizootic algorithm defined a time-series of successive intervals of epizootic and inter-epizootic raccoon rabies. The odds of diagnosing a rabid cat during the first epizootic of raccoon rabies was 12 times greater than for the period prior to epizootic emergence. After the first raccoon epizootic, the risk for cat rabies remained elevated at levels six- to seven-fold above baseline. Increased monthly counts of rabid raccoons and skunks and decreasing human population density increased the probability of cat rabies in most models. Forecasting of the public health and veterinary burden of rabies and assessing the economics of control programmes, requires linking outcomes to dynamic, but predictable, changes in the temporal evolution of rabies epizootics.

Spatiotemporal analysis of epizootic raccoon rabies propagation in Connecticut, 1991-1995.

The quantitative analysis of pathogen transmission within its specific spatial context should improve our ability to predict and control the epizootic spread of that disease. We compared two methods for calibrating the effect of local, spatially distributed environmental heterogeneities on disease spread. Using the time-of-first-appearance of raccoon rabies across the 169 townships in Connecticut, we estimated local spatial variation in township-to-township transmission rate using Trend Surface Analysis (TSA) and then compared these estimates with those based on an earlier probabilistic simulation using the same data. Both the probabilistic simulation and the TSA reveal significant reduction in transmission when local spatial domains are separated by rivers. The probabilistic simulation suggested that township-to-township transmission was reduced sevenfold for townships separated by a river. The global effect of this sevenfold reduction is to increase the time-to-first-appearance in the eastern townships of Connecticut by approximately 29.7% (spread was from west to east). TSA revealed a similar effect of rivers with an overall reduction in rate of local propagation due to rivers of approximately 22%. The 7.7% difference in these two estimates reveals slightly different aspects of the spatial dynamics of this epizootic. Together, these two methods can be used to construct an overall picture of the combined effects of local spatial variation in township-to-township transmission on patterns of local rate of propagation at scales larger than the immediate nearest neighboring townships.

Predicting the local dynamics of epizootic rabies among raccoons in the United States.

Mathematical models have been developed to explore the population dynamics of viral diseases among wildlife. However, assessing the predictions stemming from these models with wildlife databases adequate in size and temporal duration is uncommon. An epizootic of raccoon rabies that began in the mid-Atlantic region of the United States in the late 1970s has developed into one of the largest and most extensive in the history of wildlife rabies. We analyzed the dynamics of local epizootics at the county level by examining a database spanning more than 20 years and including 35,387 rabid raccoons. The size, number, and periodicity of rabies epizootics among raccoons were compared with predictions derived from a susceptible, exposed, infectious, and recovered model of raccoon rabies [Coyne, J., Smith, G. & McAllister, F. E. (1989) Am. J. Vet. Res. 50, 2148-2154]. After our methods for defining epizootics were applied to solutions of the model, the time series revealed recurrent epizootics in some counties, with a median first epizootic period of 48 months. Successive epizootics declined in size and the epizootic period progressively decreased. Our reanalysis of the model predicted the initial-epizootic period of 4-5 years, with a progressive dampening of epizootic size and progressive decrease in epizootic period. The best quantitative agreement between data and model assumed low levels of immunity (1-5%) within raccoon populations, suggesting that raccoons develop little or no rabies immune class. These results encourage the use of data obtained through wildlife surveillance in assessing and refining epidemic models for wildlife diseases.

Sequential search and the influence of male quality on female mating decisions.

The patterns of phenotypic association between mated males and females depend on the decision rules that individuals employ during search for a mate. We generalize the sequential search rule and examine how the shape of the function that relates a male character to the benefit of a mating decision influences the threshold value of the male trait that induces females to terminate search. If the fitness function is linear the optimal threshold value of a male character increases with the slope of the function. The phenotypic threshold criterion declines, all else being equal, if the fitness function is made more concave (or less convex) by an increase of the risk of the function. The expression of the trait in females has no effect on the optimal threshold value of a male character if the fitness function is linear and phenotypic values combine additively to influence the benefit of a mating decision; the phenotypic threshold criterion is ubiquitous among females. A convex fitness function induces females with high trait values to adopt a relatively high phenotypic threshold criterion, whereas a concave fitness function induces such females to adopt a low threshold value for the male trait. Thus, linear, convex and concave fitness functions effect random, assortative and disassortative combinations of phenotypes among mated individuals, respectively. Changes of female search behavior induced by changes of the distribution of a male character similarly depend on the shape of the fitness function. A variance-preserving increase of male trait values produces a relatively small increase of the threshold criterion for the male character if the fitness function is concave, relative to conditions in which the fitness function is either linear or convex. Our results suggest that a sequential search rule can in principle induce the kinds of mating patterns observed in nature and that the phenotypic association between mated individuals is likely to depend on how a male character translates into fitness, the distribution of the trait among males and attributes of searching females.

Transmission bottlenecks as determinants of virulence in rapidly evolving pathogens.

Transmission bottlenecks occur in pathogen populations when only a few individual pathogens are transmitted from one infected host to another in the initiation of a new infection. Transmission bottlenecks can dramatically affect the evolution of virulence in rapidly evolving pathogens such as RNA viruses. Characterizing pathogen diversity with the quasispecies concept, we use analytical and simulation methods to demonstrate that severe bottlenecks are likely to drive down the virulence of a pathogen because of stochastic loss of the most virulent pathotypes, through a process analogous to Muller's ratchet. We investigate in this process the roles of host population size, duration of within-host viral replication, and transmission bottleneck size. We argue that the patterns of accumulation of deleterious mutation may explain differing levels of virulence in vertically and horizontally transmitted diseases.

Toward a cognitive ecology.

The emergence of cognitive psychology as the dominant approach to understanding human behaviors and actions acknowledges the importance of internal mental operations in generating specific behavioral responses to sets of external stimuli. Traditional behaviorist interpretations that rely primarily on external inputs as the precursors of action have been largely replaced by cognitive approaches. The main intent of this article is to outline the major areas that require exploration if we wish to apply fully the principles and insight of cognitive science to behavioral ecology.

Animal choice behavior and the evolution of cognitive architecture.

Animals process sensory information according to specific computational rules and, subsequently, form representations of their environments that form the basis for decisions and choices. The specific computational rules used by organisms will often be evolutionarily adaptive by generating higher probabilities of survival, reproduction, and resource acquisition. Experiments with enclosed colonies of bumblebees constrained to foraging on artificial flowers suggest that the bumblebee's cognitive architecture is designed to efficiently exploit floral resources from spatially structured environments given limits on memory and the neuronal processing of information. A non-linear relationship between the biomechanics of nectar extraction and rates of net energetic gain by individual bees may account for sensitivities to both the arithmetic mean and variance in reward distributions in flowers. Heuristic rules that lead to efficient resource exploitation may also lead to subjective misperception of likelihoods. Subjective probability formation may then be viewed as a problem in pattern recognition subject to specific sampling schemes and memory constraints.