Within-host dynamics and random duration of pathogen infection: Implications for between-host transmission.

Taking an ecological perspective, this paper reports theoretical and empirical results concerning fatal bacterial infections of adult insects. Two models, each combining deterministic and stochastic elements, characterize how the pathogen's dynamics might govern an infected host's mortality rate. We analyze the models in detail for exponential pathogen growth, and apply them to observed insect mortality when the pathogen's growth is unregulated. We then allow bacteriophage to generate fluctuations in the within-host pathogen density; we demonstrate that only one of our models matches host mortality rates when pathogen growth is regulated by phage. We generalize our results on mortality hazard of individual hosts to analyze how random duration of the infectious period can combine with probabilistic transmission events to affect between-host transmission.

Assortative Mating: Encounter-Network Topology and the Evolution of Attractiveness.

We model a social-encounter network where linked nodes match for reproduction in a manner depending probabilistically on each node's attractiveness. The developed model reveals that increasing either the network's mean degree or the "choosiness" exercised during pair formation increases the strength of positive assortative mating. That is, we note that attractiveness is correlated among mated nodes. Their total number also increases with mean degree and selectivity during pair formation. By iterating over the model's mapping of parents onto offspring across generations, we study the evolution of attractiveness. Selection mediated by exclusion from reproduction increases mean attractiveness, but is rapidly balanced by skew in the offspring distribution of highly attractive mated pairs.

Fisher waves and front roughening in a two-species invasion model with preemptive competition.

We study front propagation when an invading species competes with a resident; we assume nearest-neighbor preemptive competition for resources in an individual-based, two-dimensional lattice model. The asymptotic front velocity exhibits an effective power-law dependence on the difference between the two species' clonal propagation rates (key ecological parameters). The mean-field approximation behaves similarly, but the power law's exponent slightly differs from the individual-based model's result. We also study roughening of the front, using the framework of nonequilibrium interface growth. Our analysis indicates that initially flat, linear invading fronts exhibit Kardar-Parisi-Zhang (KPZ) roughening in one transverse dimension. Further, this finding implies, and is also confirmed by simulations, that the temporal correction to the asymptotic front velocity is of O(t(-2/3)).

Lyme disease in New York State: spatial pattern at a regional scale.

Lyme disease occurs commonly in New York State, but its geographic distribution is heterogeneous. Over each of nine consecutive years, incidence rates from 57 New York State counties were subjected to spatial autocorrelation analysis. Although the epidemic advanced during the study period, the analyses reveal a consistent pattern of spatial dependence. The correlation distance, the distance over which incidence rates covary positively, remained near 120 km over the nine years. A local spatial analysis around Westchester County, a major disease focus, indicated that the global correlation distance matched the extent of the most intense local clustering; statistically weaker clustering extended to 200 km from Westchester. Analyzing the spatial character of the epidemic may reveal the epizootic processes underlying patterns in human infection, and may help identify a spatial scale for regional control of disease.

Host spatial heterogeneity and the spread of vector-borne infection.

We analyze how spatial heterogeneity in host density affects the advance of vector-borne disease. Infection requires vector infestation. The vector spreads only between hosts occupying the same neighborhood, and the number of hosts varies randomly among neighborhoods. Simulation of a spatially detailed model shows that increasing heterogeneity in host abundance reduces pathogen prevalence. Clumping of hosts can limit the advance of the vector, which inhibits the spread of infection indirectly. Clumping can also increase the chance that the pathogen and vector become physically separated during the initial phase of the epidemic process. The latter limitation on the pathogen's spread, in our simulations, is restricted to small interaction neighborhoods. A mean-field model, which does not maintain spatial correlations between sites, approximates simulation results when hosts are arrayed uniformly, but overestimates infection prevalence when hosts are aggregated. A pair approximation, which includes some of the simulation model's spatial correlations, better describes the vector infestation frequencies across host spatial dispersions.

Lyme disease: self-regulation and pathogen invasion.

Ecological interactions underlying the epidemic of Lyme disease involve a spirochete, a tick (with larval, nymph and adult stages), and two (or more) vertebrate hosts. Juvenile ticks ordinarily feed on mice; adult ticks feed on deer. Mice acquire the spirochete from infected nymphs and then pass the infection to larvae of the next tick generation. Lyme disease may result when a human is inadvertently bitten by an infectious nymph. Our model of the Lyme phenomenon counts the total number of ticks in each stage, the numbers of infected ticks by stage, and the number of infected mice. We fix the total population sizes of deer and mice, assume the ticks self-regulate, and solve the homogeneous-mixing case for equilibrium abundances. A local stability analysis identifies a condition where extinction of the spirochete is stable. Reversing this condition implies that the spirochete can invade the system of ticks and vertebrate hosts. When the spirochete can invade, a positive equilibrium number of infected organisms is locally stable. Spirochete invasion is promoted by a sufficient density of mice suffering low mortality, high susceptibility to infection in both mice and ticks, a high attack rate of ticks on mice, a high density of larval ticks, and low mortality among tick nymphs. Low mouse mortality allows the frequency of infection among nymphs to approach an individual tick's susceptibility when feeding on an infected mouse.

Host spatial heterogeneity and extinction of an SIS epidemic.

Spatially explicit epidemic models explore population-level consequences of interactions between neighboring infectious and susceptible individuals. Most such models equate local and global host density, so that each individual interacts with the same number of neighbors. But many natural populations exhibit heterogeneity in local abundance. Therefore, we let host dispersion vary from uniform to clumped in a spatial epidemic with recovery. We analytically approximated the epidemic with a branching process to show how the probability of pathogen extinction could depend on the degree of host clumping. We then simulated the detailed model across a range of parameter combinations. Both approaches to the problem indicate that host spatial aggregation strongly increases the chance of pathogen extinction.

Parallel discrete event simulation of Lyme disease.

Our research concerns the dynamic processes underlying the rapid increase in the geographic distribution of Lyme disease, currently the most frequently reported vector-borne disease of humans in the United States [10, 1]. More specifically, we ask how spatially localized ecological interactions drive the Lyme disease epidemic at extended spatial and temporal scales. We have developed a parallel discrete event simulation system in C++ for the IBM SP2. The simulation model discussed here models the mouse-tick interaction, an essential element of the epidemic's ecology. The main entities of the simulation are ticks in various stages of development (larval, nymphal, and adult) and mice. We track the behavior of mice and the spread of disease over the course of 180 days (late spring, summer, and early fall). Our goal is to understand patterns in the Lyme disease epidemic at the regional scale through studying the spread of the pathogen across a single white-footed mouse deme.

Foraging choice in laboratory rats: Constant vs. variable delay.

Deprived animals choosing between a variable delay (with mean t ) and a constant delay of t s prior to availability of food usually prefer the variable delay. Models of discounted future rewards predict such preference. For comparison we write a model assuming that a forager minimizes the probability that its total food intake falls short of a fixed requirement. This model predicts preference for the constant delay at sufficiently high average feeding rates. In a test of the models, laboratory rats (Rattus norvegicus ) chose between a constant t s delay and a variable option with equiprobable delays of 1 and (2t -1)s. Each subject was presented with the same sequence of mean delays. Each delay was experienced by the subjects for seven consecutive test days. Between the first and the fourth test day, a subject's body weight was decreased from 85 to 75 percent of free- feeding weight. Between the fourth and the seventh test day, a subject's body weight was increased to 85 percent of free-feeding weight. As t increased from 5 to 50 s, subjects first preferred the constant delay and then came to prefer the variable delay. Thereafter, as t was decreased to 5 s, subjects retained preference for the variable delay, but the strength of that preference declined at t decreased. Short-term variation in body weight, at a given value of t , did not influence preference significantly. Despite the rats' initial preference for constant delays, we tentatively conclude that our results appear more consistent with the discounting model than with the energy budget model.