Noise and Nonlinearity in Measles Epidemics: Combining Mechanistic and Statistical Approaches to Population Modeling

We present and evaluate an approach to analyzing population dynamics data using semimechanistic models. These models incorporate reliable information on population structure and underlying dynamic mechanisms but use nonparametric surface-fitting methods to avoid unsupported assumptions about the precise form of rate equations. Using historical data on measles epidemics as a case study, we show how this approach can lead to better forecasts, better characterizations of the dynamics, and better understanding of the factors causing complex population dynamics relative to either mechanistic models or purely descriptive statistical time-series models. The semimechanistic models are found to have better forecasting accuracy than either of the model types used in previous analyses when tested on data not used to fit the models. The dynamics are characterized as being both nonlinear and noisy, and the global dynamics are clustered very tightly near the border of stability (dominant Lyapunov exponent λ < 0). However, locally in state space the dynamics oscillate between strong short-term stability and strong short-term chaos (i.e., between negative and positive local Lyapunov exponents). There is statistically significant evidence for short-term chaos in all data sets examined. Thus the nonlinearity in these systems is characterized by the variance over state space in local measures of chaos versus stability rather than a single summary measure of the overall dynamics as either chaotic or nonchaotic

Mathematical Biology at an Undergraduate Liberal Arts College

Since 2002 we have offered an undergraduate major in Mathematical Biology at Harvey Mudd College. The major was developed and is administered jointly by the mathematics and biology faculty. In this paper we describe the major, courses, and faculty and student research and discuss some of the challenges and opportunities we have experienced

A mean-field version of the Nicodemi-Prisco SSB model for X-chromosome inactivation

Nicodemi and Prisco recently proposed a model for X-chromosome inactivation in mammals, explaining this phenomenon in terms of a spontaneous symmetry-breaking mechanism [{\it Phys. Rev. Lett.} 99 (2007), 108104]. Here we provide a mean-field version of their model

Effects of rapid prey evolution on predator-prey cycles

We study the qualitative properties of population cycles in a predator-prey system where genetic variability allows contemporary rapid evolution of the prey. Previous numerical studies have found that prey evolution in response to changing predation risk can have major quantitative and qualitative effects on predator-prey cycles, including: (i) large increases in cycle period, (ii) changes in phase relations (so that predator and prey are cycling exactly out of phase, rather than the classical quarter-period phase lag), and (iii) "cryptic" cycles in which total prey density remains nearly constant while predator density and prey traits cycle. Here we focus on a chemostat model motivated by our experimental system [Fussmann et al. 2000,Yoshida et al. 2003] with algae (prey) and rotifers (predators), in which the prey exhibit rapid evolution in their level of defense against predation. We show that the effects of rapid prey evolution are robust and general, and furthermore that they occur in a specific but biologically relevant region of parameter space: when traits that greatly reduce predation risk are relatively cheap (in terms of reductions in other fitness components), when there is coexistence between the two prey types and the predator, and when the interaction between predators and undefended prey alone would produce cycles. Because defense has been shown to be inexpensive, even cost-free, in a number of systems [Andersson and Levin 1999, Gagneux et al. 2006,Yoshida et al. 2004], our discoveries may well be reproduced in other model systems, and in nature. Finally, some of our key results are extended to a general model in which functional forms for the predation rate and prey birth rate are not specified.Comment: 35 pages, 8 figure

Venezuela, April 2002: Coup or Popular Rebellion? The Myth of a United Venezuela

This article assesses the merits of opposing National Assembly reports into the coup against President Chavez of Venezuela in April 2002. Looking at the historical context and the content of the reports, it argues that the two opposing accounts reflect a class division that has always existed in Venezuela but has been officially denied. It concludes that a possible exit from the stalemate could be that the opposition accept the reality of this class division and therefore the Chavez government as a legitimate representative of the popular classes. This, however, is unlikely in the present circumstances

Integrating evolution into ecological modelling: accommodating phenotypic changes in agent based models.

PMCID: PMC3733718This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Evolutionary change is a characteristic of living organisms and forms one of the ways in which species adapt to changed conditions. However, most ecological models do not incorporate this ubiquitous phenomenon. We have developed a model that takes a 'phenotypic gambit' approach and focuses on changes in the frequency of phenotypes (which differ in timing of breeding and fecundity) within a population, using, as an example, seasonal breeding. Fitness per phenotype calculated as the individual's contribution to population growth on an annual basis coincide with the population dynamics per phenotype. Simplified model variants were explored to examine whether the complexity included in the model is justified. Outputs from the spatially implicit model underestimated the number of individuals across all phenotypes. When no phenotype transitions are included (i.e. offspring always inherit their parent's phenotype) numbers of all individuals are always underestimated. We conclude that by using a phenotypic gambit approach evolutionary dynamics can be incorporated into individual based models, and that all that is required is an understanding of the probability of offspring inheriting the parental phenotype

Treatment outcomes of new tuberculosis patients hospitalized in Kampala, Uganda: a prospective cohort study.

BACKGROUND: In most resource limited settings, new tuberculosis (TB) patients are usually treated as outpatients. We sought to investigate the reasons for hospitalisation and the predictors of poor treatment outcomes and mortality in a cohort of hospitalized new TB patients in Kampala, Uganda. METHODS AND FINDINGS: Ninety-six new TB patients hospitalised between 2003 and 2006 were enrolled and followed for two years. Thirty two were HIV-uninfected and 64 were HIV-infected. Among the HIV-uninfected, the commonest reasons for hospitalization were low Karnofsky score (47%) and need for diagnostic evaluation (25%). HIV-infected patients were commonly hospitalized due to low Karnofsky score (72%), concurrent illness (16%) and diagnostic evaluation (14%). Eleven HIV uninfected patients died (mortality rate 19.7 per 100 person-years) while 41 deaths occurred among the HIV-infected patients (mortality rate 46.9 per 100 person years). In all patients an unsuccessful treatment outcome (treatment failure, death during the treatment period or an unknown outcome) was associated with duration of TB symptoms, with the odds of an unsuccessful outcome decreasing with increasing duration. Among HIV-infected patients, an unsuccessful treatment outcome was also associated with male sex (P = 0.004) and age (P = 0.034). Low Karnofsky score (aHR = 8.93, 95% CI 1.88 - 42.40, P = 0.001) was the only factor significantly associated with mortality among the HIV-uninfected. Mortality among the HIV-infected was associated with the composite variable of CD4 and ART use, with patients with baseline CD4 below 200 cells/µL who were not on ART at a greater risk of death than those who were on ART, and low Karnofsky score (aHR = 2.02, 95% CI 1.02 - 4.01, P = 0.045). CONCLUSION: Poor health status is a common cause of hospitalisation for new TB patients. Mortality in this study was very high and associated with advanced HIV Disease and no use of ART

Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog

How Microbial Community Composition Regulates Coral Disease Development

Modeling reveals how rapid overgrowth by pathogenic microbes in the mucus layer surrounding corals, which often occurs under temporary stressful conditions, can persist long after environmental conditions return to normal