Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session N23: Focus Session: Methods of Statistical Physics in Population Dynamics and Epidemiology |
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Sponsoring Units: GSNP DBP Chair: Len Sander, University of Michigan Room: LACC 410 |
Wednesday, March 23, 2005 8:00AM - 8:36AM |
N23.00001: Statistical physics applied to ecology Invited Speaker: Understanding an ecosystem is a formidable many-body problem. One has an interacting system, made up of individuals of various species with imperfectly known interactions, mainly governed by chance and characterized by a wide range of spatial and temporal scales. For example, in tropical forests across the globe, ecologists have been able to measure certain quantities such as the relative species abundance distribution, the species area relationship, and beta diversity, the probability that two trees separated by a given distance belong to the same species. In order to make progress, it is important to distill what one hopes are the essential ingredients of an ecosystem and incorporate them in tractable models whose predictions can then be compared with the observed data. Such an interplay between empirical data and theory is useful for the formulation of realistic models of ecosystems. A summary of recent work along these lines will be presented. Co-author: Amos Maritan Collaborators: John Damuth, Fangliang He, Steve Hubbell, Andrea Rinaldo, Igor Volkov and Tommaso Zillio [Preview Abstract] |
Wednesday, March 23, 2005 8:36AM - 8:48AM |
N23.00002: Phase Transitions and Fluctuations in Lattice Predator-Prey Models with Site Restrictions Mauro Mobilia, Ivan Georgiev, Uwe Taeuber Studying the effects of spatial constraints and stochastic fluctuations on a class of predator-prey models with two species defined on a lattice it has been shown that the celebrated Lotka-Volterra's mean-field rate equation picture is invalidated. In this contribution, we report how site occupation constraints, modeling locally limited resources and the range of the interaction between species can lead to the emergence of an active-to-absorbing phase transition or to a first order phase transition. In particular, ecologically motivated models with nearest and next-nearest neighbor interactions are discussed and shown to display both an absorbing and an active steady state. In the latter case, where predators and prey coexist, the classical limit cycles or centers are replaced by either nodes or foci, leading to damped oscillatory behavior of the densities of predators and prey in the thermodynamic limit and to stationary configuration displaying complex spatiotemporal patterns. We discuss the validity of the analytic approach against numerical simulations and the subtle role played by the fluctuations and by the degree of ``stirring'' of the system. [Preview Abstract] |
Wednesday, March 23, 2005 8:48AM - 9:00AM |
N23.00003: Absorbing multicultural states in the Axelrod model Federico Vazquez, Sidney Redner We determine the ultimate fate of a limit of the Axelrod model that consists of a population of leftists, centrists, and rightists. In an elemental interaction between agents, a centrist and a leftist can both become centrists or both become leftists with equal rates (similarly for a centrist and a rightist), but leftists and rightists do not interact. This interaction is applied repeatedly until the system can no longer evolve. The constraint between extremists can lead to a frustrated final state where the system consists of only leftists and rightists. In the mean field limit, we can view the evolution of the system as the motion of a random walk in the 3-dimensional space whose coordinates correspond to the density of each species. We find the exact final state probabilities and the time to reach consensus by solving for the first-passage probability of the random walk to the corresponding absorbing boundaries. The extension to a larger number of states will be discussed. This approach is a first step towards the analytic solution of Axelrod-like models. [Preview Abstract] |
Wednesday, March 23, 2005 9:00AM - 9:12AM |
N23.00004: Nucleation and Spread of an Invasive Allele Gyorgy Korniss, Joseph Yasi, Thomas Caraco We analyze a prototypical discrete spatial model for the spread of an invasive allele when individuals compete preemptively for common limiting resources. Initially, the population is genetically monomorphic with the resident allele at high density. The invasive allele is introduced through rare, but recurrent, mutation. The mutant allele is the better competitor (has an individual-level advantage) but its spread is limited by the local availability of resources. We find that each successful introduction of the mutant leads to strong spatial clustering. Spatial patterns in simulation resemble nucleation and subsequent growth, articulately described by Avrami's law in sufficiently large systems\footnote{G. Korniss and T. Caraco, J. Theor. Biol. (in press, 2004); http://www.rpi.edu/~korniss/Research/JTB04.pdf}. [Preview Abstract] |
Wednesday, March 23, 2005 9:12AM - 9:24AM |
N23.00005: Coupling ecological and evolutionary dynamics in a stochastic model of multiple-gene interactions Ralph DeSimone, Ankana Boondirek, Timothy Newman In this talk we discuss the ``genome template model'' (GTM) which we have recently introduced in order to connect fluctuations in a genotypically heterogeneous population to evolutionary processes such as adaptation and selection. This connection is explicitly made by modeling reproduction and mortality as polygenic traits, coupled, within each individual, to an underlying genome. We will highlight two properties of the GTM: i) high fitness ``ridges'' in genotype space which are a direct consequence of gene interactions, and ii) evolution of spatial polymorphism on environmental gradients. [Preview Abstract] |
Wednesday, March 23, 2005 9:24AM - 9:36AM |
N23.00006: Extinction Times for Birth-Death Processes: Continuum Asymptotics and the failure of the Fokker-Planck Approximation Charles R. Doering, Khachik V. Sargsyan, Leonard M. Sander We consider extinction times for a class of birth-death processes commonly found in applications where there is a control parameter defining a threshold. Below the threshold, the population quickly becomes extinct; above, it persists for a long time. We give an exact expression for the mean time to extinction in the discrete case and derive its asymptotic expansion for large values of the population scale. We present results below the threshold, at the threshold, and above the threshold, observing that the Fokker-Planck approximation is valid only quite near the threshold. We compare the asymptotic results to exact numerical evaluations for the Susceptible-Infected-Susceptible (SIS) epidemic model. This is an interesting example of the delicate relationship between discrete and continuum treatments of the same problem. [Preview Abstract] |
Wednesday, March 23, 2005 9:36AM - 10:12AM |
N23.00007: Infectious diseases in space and time: noise and nonlinearity in epidemiological dynamics Invited Speaker: I illustrate the impact of noise and nonlinearity on the spatio-temporal dynamics and evolution of epidemics using mathematical models and analyses of detailed epidemiological data from childhood infections, such as measles. [Preview Abstract] |
Wednesday, March 23, 2005 10:12AM - 10:24AM |
N23.00008: Pandemic Diseases and the Aviation Network – SARS, a case study Lars Hufnagel, Dirk Brockmann, Theo Geisel We investigate the mechanisms of the worldwide spread of infectious diseases in a modern world in which humans travel on all scales. We introduce a probabilistic model which accounts for the worldwide spread of infectious diseases on the global aviation network. The analysis indicates that a forecast of the geographical spread of an epidemic is indeed possible, provided that local dynamical parameters of the disease such as the basic reproduction number are known. The model consists of local stochastic infection dynamics and stochastic transport of individuals on the worldwide aviation network which takes into account over 95% of the entire the national and international civil aviation traffic. Our simulations of the SARS outbreak are in surprisingly good agreement with published case reports. Despite the fact that the system is stochastic with a high number of degrees of freedom the outcome of a single simulation exhibits only a small magnitude of variability. We show that this is due to the strong heterogeneity of the network ranging from a few two over 25,000 passengers between nodes of the network. Thus, we propose that our model can be employed to predict the worldwide spread of future pandemic diseases and to identify endangered regions in advance. Based on the connectivity of the aviation network we evaluate the performance of different control strategies and show that a quick and focused reaction is essential to inhibit the global spread of infectious diseases. [Preview Abstract] |
Wednesday, March 23, 2005 10:24AM - 10:36AM |
N23.00009: Respiratory-borne Disease Outbreaks in Populations: Contact Networks and the Spread of Disease Babak Pourbohloul, Lauren A. Meyers, Mark E.J. Newman, Danuta M. Skowronski, Robert C. Brunham A large class of infectious diseases spread through direct person-to-person contact. Traditional ``compartmental'' modeling in epidemiology assumes that in population groups every individual has an equal chance of spreading the disease to every other. The patterns of these contacts, however, tend to be highly heterogeneous. Explicit models of the patterns of contact among individuals in a community, contact network models, underlie a powerful approach to predicting and controlling the spread of such infectious disease and provide detailed and valuable insight into the fate and control of an outbreak. We use contact network epidemiology to predict the impact of various control policies for both a mildly contagious disease such as SARS and a more highly contagious disease such as smallpox. We demonstrate how integrating these tools into public health decision-making should facilitate more rational strategies for managing newly emerging diseases, bioterrorism and pandemic influenza in situations where empirical data are not yet available to guide decision making. [Preview Abstract] |
Wednesday, March 23, 2005 10:36AM - 10:48AM |
N23.00010: Dynamical Epidemic Suppression Using Stochastic Prediction and Control Ira Schwartz, Lora Billings, Erik Bollt We consider the effects of noise on a model of epidemic outbreaks, where the outbreaks appear randomly. Using a constructive transition approach that predicts large outbreaks prior to their occurrence, we derive an adaptive control scheme that prevents large outbreaks from occurring. The theory is applicable to a wide range of stochastic processes with underlying deterministic structure. [Preview Abstract] |
Wednesday, March 23, 2005 10:48AM - 11:00AM |
N23.00011: Chaotic desynchronization of multistrain diseases Leah Shaw, Lora Billings, Marie McCrary, Ira Schwartz Dengue fever, a multi-strain disease, has four distinct co-existing serotypes (strains). The serotypes interact by antibody-dependent enhancement (ADE), in which infection with a single serotype is asymptomatic, but contact with a second serotype leads to serious illness accompanied by greater infectivity. It has been observed from serotype data that outbreaks of the four serotypes occur asynchronously (Nisalak et al., Am. J. Trop. Med. Hyg. 68: 192). We developed a compartmental model and did bifurcation analysis for multiple serotypes with ADE. Both autonomous and seasonally driven versions were studied. For sufficiently small ADE, we find that the number of infectives of each serotype synchronizes, with outbreaks occurring in phase. However, when the ADE increases past a threshold, the system becomes chaotic, and infectives of each serotype desynchronize. [Preview Abstract] |
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