Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session Z28: Methods of Statistical Physics, Population Dynamics and Epidemiology |
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Sponsoring Units: DBP GSNP Chair: Vadim Smelyanskiy, NASA Ames Research Center Room: Baltimore Convention Center 325 |
Friday, March 17, 2006 11:15AM - 11:27AM |
Z28.00001: Mathematical Modeling of the Dynamics of \textit{Salmonella} Cerro Infection in a US Dairy Herd Prem Chapagain, Jo Ann Van Kessel, Jeffrey Karns, David Wolfgang, Ynte Schukken, Yrjo Grohn Salmonellosis has been one of the major causes of human foodborne illness in the US. The high prevalence of infections makes transmission dynamics of \textit{Salmonella} in a farm environment of interest both from animal and human health perspectives. Mathematical modeling approaches are increasingly being applied to understand the dynamics of various infectious diseases in dairy herds. Here, we describe the transmission dynamics of \textit{Salmonella} infection in a dairy herd with a set of non-linear differential equations. Although the infection dynamics of different serotypes of \textit{Salmonella} in cattle are likely to be different, we find that a relatively simple SIR-type model can describe the observed dynamics of the \textit{Salmonella enterica} serotype Cerro infection in the herd. [Preview Abstract] |
Friday, March 17, 2006 11:27AM - 11:39AM |
Z28.00002: Desynchronization and spatial effects in multistrain diseases Leah Shaw, Lora Billings, Ira Schwartz Dengue fever, a multistrain 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. We present a compartmental model for multiple serotypes with ADE, and consider autonomous, seasonally driven, and stochastic versions of the model. Spatial effects are included in a multipatch model. We observe desynchronization between outbreaks of the different serotypes, as well as desynchronization between spatially distinct regions. [Preview Abstract] |
Friday, March 17, 2006 11:39AM - 11:51AM |
Z28.00003: Improved Epidemic Path Predictability in Complex Networks Markus Loecher, Jim Kadtke We apply recent results on random walkers to the analysis of idealized epidemic outbreaks in scale-free networks. By replacing the node degree with the {\it random walk centrality} we observe a refined hierarchical cascade leading to a greatly enhanced predictability for the order of infected nodes. We confirm our model results on data from real-world Internet maps at the autonomous system level. The present results are highly relevant for the advancement of dynamic and adaptive strategies that aim to mitigate network attacks. [Preview Abstract] |
Friday, March 17, 2006 11:51AM - 12:27PM |
Z28.00004: The scaling laws of human travel - A message from George Invited Speaker: In the light of increasing international trade, intensified human mobility and an imminent influenza A epidemic the knowledge of dynamical and statistical properties of human travel is of fundamental importance. Despite its crucial role, a quantitative assessment of these properties on geographical scales remains elusive and the assumption that humans disperse diffusively still prevails in models. I will report on a solid and quantitative assessment of human travelling statistics by analysing the circulation of bank notes in the United States. Based on a comprehensive dataset of over a million individual displacements we find that dispersal is anomalous in two ways. First, the distribution of travelling distances decays as a power law, indicating that trajectories of bank notes are reminiscent of scale free random walks known as L\'evy flights. Secondly, the probability of remaining in a small, spatially confined region for a time $T$ is dominated by algebraic tails which attenuate the superdiffusive spread. We show that human travel can be described mathematically on many spatiotemporal scales by a two parameter continuous time random walk model to a surprising accuracy and conclude that human travel on geographical scales is an ambivalent effectively superdiffusive process. [Preview Abstract] |
Friday, March 17, 2006 12:27PM - 12:39PM |
Z28.00005: Prediction and predictability of global epidemics: the role of the airline transportation network Vittoria Colizza, Alain Barrat, Marc Barthelemy, Alessandro Vespignani The systematic study of large-scale networks has unveiled the ubiquitous presence of connectivity patterns characterized by large scale heterogeneities and unbounded statistical fluctuations. These features affect dramatically the behavior of the diffusion processes occurring on networks, determining the ensuing statistical properties of their evolution pattern and dynamics. We present a stochastic computational framework for the forecast of global epidemics that considers the complete world-wide air travel infrastructure complemented with census population data. We address two basic issues in global epidemic modeling: i) We study the role of the large scale properties of the airline transportation network in determining the global diffusion pattern of emerging diseases; ii) We evaluate the reliability of forecasts and outbreak scenarios with respect to the intrinsic stochasticity of disease transmission and traffic flows. In order to address these issues we define a set of novel quantitative measures able to characterize the level of heterogeneity and predictability of the epidemic pattern. These measures may be used for the analysis of containment policies and epidemic risk assessment. [Preview Abstract] |
Friday, March 17, 2006 12:39PM - 12:51PM |
Z28.00006: Success of mutants in an evolutionary game in finite populations Tibor Antal, Istvan Scheuring A stochastic evolutionary dynamics of two strategies given by $2\times 2$ matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire population. The process is discussed in the framework of a random walk with site dependent hopping rates. The time of fixation is found to be identical for both strategies in any particular game. The asymptotic behavior of the fixation time and fixation probabilities in the large population size limit is also discussed. We show that fixation is fast when there is at least one pure evolutionary stable strategy (ESS) in the infinite population size limit, while fixation is slow when the ESS is the coexistence of the two strategies. [Preview Abstract] |
Friday, March 17, 2006 12:51PM - 1:03PM |
Z28.00007: Invasion of mutants in an evolutionary process on a graph. Vishal Sood, Tibor Antal We study the Moran process (MP) on an undirected graph. The MP has been studied on the complete graph and lattices extensively. Remarkably the fixation probability of the mutants is the same for all undirected degree-regular graphs. However, this is not true for degree-heterogeneous graphs. Some graphs can enhance the fixation probabilities over the degree-regular graphs. We derive fixation probabilities for general graphs when the mutants have a small advantage over the resident population. For the general bias case, we derive exact results for the bipartite graphs and discuss the structure of graphs where such a result can be applicable. [Preview Abstract] |
Friday, March 17, 2006 1:03PM - 1:15PM |
Z28.00008: Seeing beyond invisible with noise: application to populational biology Dmitry Luchinsky, Vadim Smelyanskiy The problem of determining dynamical models and trajectories that describe observed timeseries data (dynamical inference) allowing for the understanding, prediction and possibly control of complex systems in nature is of great interest in a variety of fields. Often, however, in multidimensional systems only part of the system’s dynamical variables can be measured directly. The measurements are usually corrupted by noise and the dynamics is complicated by interplay of nonlinearity and random perturbations. We solve the problem of dynamical inference in these general settings by applying a path-integral approach to fuctuational dynamics, and show that, given the measurements, the most probable system trajectory can be obtained from the solution of the certain auxiliary Hamiltonian problem in which measured data act effectively as a control force driving algorithm towards the most probable solution. We illustrate the efficiency of the approach by solving an intensively studied problem from the population dynamics of a predator-prey system where the prey populations may be observed while the number of predators is difficult or impossible to estimate. We apply our approach to recover both the unknown dynamics of predators and model parameters (including parameters that are traditionally very difficult to estimate) directly from real data measurements of the prey dynamics. [Preview Abstract] |
Friday, March 17, 2006 1:15PM - 1:27PM |
Z28.00009: Eigen model with general fitness functions and degradation rates Chin-Kun Hu, David B. Saakian We present an exact solution of Eigen's quasispecies model with a general degradation rate and fitness functions, including a square root decrease of fitness with increasing Hamming distance from the wild type. The found behavior of the model with a degradation rate is analogous to a viral quasi-species under attack by the immune system of the host. Our exact solutions also revise the known results of neutral networks in quasispecies theory. To explain the existence of mutants with large Hamming distances from the wild type, we propose three different modifications of the Eigen model: mutation landscape, multiple adjacent mutations, and frequency-dependent fitness in which the steady state solution shows a multi-center behavior. [Preview Abstract] |
Friday, March 17, 2006 1:27PM - 1:39PM |
Z28.00010: Combining a total cell population growth and cell population dynamics in the presence of anti-cancer agents Mitra Shojania Feizabadi A two-compartment Webb-Gyllenberg model describes the population dynamics of proliferating and quiescent cancer cells. ~Combination of the total cell growth curve and the two-compartment model yields an analytical solution for the behavior of proliferating subpopulation and the net transition rate between proliferating and quiescent cells as a function of time. This work presents a qualitative model for drug interaction with cancer cells in the Webb-Gyllenberg model. ~The drug is assumed to kill all cell types, each at a specific rate. Considering the total cell population growth in the presence of the drug, the behavior and the size of proliferating and quiescence subpopulations, as well as the related transition rates have been investigated. [Preview Abstract] |
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