Modeling colony collapse disorder in honeybees as a contagion.

Honeybee pollination accounts annually for over $14 billion in United States agriculture alone. Within the past decade there has been a mysterious mass die-off of honeybees, an estimated 10 million beehives and sometimes as much as 90% of an apiary. There is still no consensus on what causes this phenomenon, called Colony Collapse Disorder, or CCD.

Graphical analysis of evolutionary trade-off in sylvatic Trypanosoma cruzi transmission modes.

The notion of evolutionary trade-off (one attribute increasing at the expense of another) is central to the evolution of traits, well-studied especially in life-history theory, where a framework first developed by Levins illustrates how internal (genetics) and external (fitness landscapes) forces interact to shape an organism׳s ongoing adaptation. This manuscript extends this framework to the context of vector-borne pathogens, with the example of Trypanosoma cruzi (the etiological agent of Chagas׳ disease) adapting via trade-off among three different infection routes to hosts-stercorarian, vertical, and oral-in response to an epidemiological landscape that involves both hosts and vectors (where, in particular, parasite evolution depends not on parasite density but on relative host and vector densities). Using a fitness measure derived from an invasion reproductive number, this study analyzes several different trade-off scenarios in cycles involving raccoons or woodrats, including a proper three-way trade-off (two independent parameters).

A metapopulation model for sylvatic T. cruzi transmission with vector migration.

This study presents a metapopulation model for the sylvatic transmission of Trypanosoma cruzi, the etiological agent of Chagas' disease, across multiple geographical regions and multiple overlapping host-vector transmission cycles. Classical qualitative analysis of the model and several submodels focuses on the parasite's basic reproductive number, illustrating how vector migration across patches and multiple transmission routes to hosts (including vertical transmission) determine the infection's persistence in each cycle. Numerical results focus on trends in endemic [equilibrium] persistence levels as functions of vector migration rates, and highlight the significance of the different epidemiological characteristics of transmission in each of the three regions.

Sociological phenomena as multiple nonlinearities: MTBI's new metaphor for complex human interactions.

Mathematical models are well-established as metaphors for biological and epidemiological systems. The framework of epidemic modeling has also been applied to sociological phenomena driven by peer pressure, notably in two dozen dynamical systems research projects developed through the Mathematical and Theoretical Biology Institute, and popularized by authors such as Gladwell (2000). This article reviews these studies and their common structures, and identifies a new mathematical metaphor which uses multiple nonlinearities to describe the multiple thresholds governing the persistence of hierarchical phenomena, including the situation termed a "backward bifurcation'' in mathematical epidemiology, where established phenomena can persist in circumstances under which the phenomena could not initially emerge.

The mathematical and theoretical biology institute--a model of mentorship through research.

This article details the history, logistical operations, and design philosophy of the Mathematical and Theoretical Biology Institute (MTBI), a nationally recognized research program with an 18-year history of mentoring researchers at every level from high school through university faculty, increasing the number of researchers from historically underrepresented minorities, and motivating them to pursue research careers by allowing them to work on problems of interest to them and supporting them in this endeavor. This mosaic profile highlights how MTBI provides a replicable multi-level model for research mentorship.

Influence of environmental factors on college alcohol drinking patterns.

Alcohol abuse is a major problem, especially among students on and around college campuses. We use the mathematical framework of [16] and study the role of environmental factors on the long term dynamics of an alcohol drinking population. Sensitivity and uncertainty analyses are carried out on the relevant functions (for example, on the drinking reproduction number and the extinction time of moderate and heavy drinking because of interventions) to understand the impact of environmental interventions on the distributions of drinkers.

Influence of vectors' risk-spreading strategies and environmental stochasticity on the epidemiology and evolution of vector-borne diseases: the example of Chagas' disease.

Insects are known to display strategies that spread the risk of encountering unfavorable conditions, thereby decreasing the extinction probability of genetic lineages in unpredictable environments. To what extent these strategies influence the epidemiology and evolution of vector-borne diseases in stochastic environments is largely unknown. In triatomines, the vectors of the parasite Trypanosoma cruzi, the etiological agent of Chagas' disease, juvenile development time varies between individuals and such variation most likely decreases the extinction risk of vector populations in stochastic environments.

Invasion speed in cellular automaton models for T. cruzi vector migration.

The parasite Trypanosoma cruzi, known for causing Chagas' disease, is spread via insect vectors from the triatomine family. T. cruzi is maintained in sylvatic vector-host transmission cycles in certain parts of the Americas.

The role of the ratio of vector and host densities in the evolution of transmission modes in vector-borne diseases. The example of sylvatic Trypanosoma cruzi.

Pathogens may use different routes of transmission to maximize their spread among host populations. Theoretical and empirical work conducted on directly transmitted diseases suggest that horizontal (i.e.

The role of adaptations in two-strain competition for sylvatic Trypanosoma cruzi transmission.

This study presents a continuous-time model for the sylvatic transmission dynamics of two strains of Trypanosoma cruzi enzootic in North America, in order to study the role that adaptations of each strain to distinct modes of transmission (classical stercorarian transmission on the one hand, and vertical and oral transmission on the other) may play in the competition between the two strains. A deterministic model incorporating contact process saturation predicts competitive exclusion, and reproductive numbers for the infection provide a framework for evaluating the competition in terms of adaptive trade-off between distinct transmission modes. Results highlight the importance of oral transmission in mediating the competition between horizontal (stercorarian) and vertical transmission; its presence as a competing contact process advantages vertical transmission even without adaptation to oral transmission, but such adaptation appears necessary to explain the persistence of (vertically-adapted) T.

Modeling nosocomial transmission of rotavirus in pediatric wards.

Nosocomial transmission of viral and bacterial infections is a major problem worldwide, affecting millions of patients (and causing hundreds of thousands of deaths) per year. Rotavirus infections affect most children worldwide at least once before age five. We present here deterministic and stochastic models for the transmission of rotavirus in a pediatric hospital ward and draw on published data to compare the efficacy of several possible control measures in reducing the number of infections during a 90-day outbreak, including cohorting, changes in healthcare worker-patient ratio, improving compliance with preventive hygiene measures, and vaccination.

A cost-based comparison of quarantine strategies for new emerging diseases.

A classical epidemiological framework is used to provide a preliminary cost analysis of the effects of quarantine and isolation on the dynamics of infectious diseases for which no treatment or immediate diagnosis tools are available. Within this framework we consider the cost incurred from the implementation of three types of dynamic control strategies. Taking the context of the 2003 SARS outbreak in Hong Kong as an example, we use a simple cost function to compare the total cost of each mixed (quarantine and isolation) control strategy from a public health resource allocation perspective.

Alternative transmission modes for Trypanosoma cruzi.

The parasite Trypanosoma cruzi, which causes Chagas' disease, is typically transmitted through a cycle in which vectors become infected through bloodmeals on infected hosts and then infect other hosts through defecation at the sites of subsequent feedings. The vectors native to the southeastern United States, however, are inefficient at transmitting T. cruzi in this way, which suggests that alternative transmission modes may be responsible for maintaining the established sylvatic infection cycle.

Estimating contact process saturation in sylvatic transmission of Trypanosoma cruzi in the United States.

Although it has been known for nearly a century that strains of Trypanosoma cruzi, the etiological agent for Chagas' disease, are enzootic in the southern U.S., much remains unknown about the dynamics of its transmission in the sylvatic cycles that maintain it, including the relative importance of different transmission routes.

Evaluating treatment of hepatitis C for hemolytic anemia management.

The combination therapy of antiviral peg-interferon and ribavirin has evolved as one of the better treatments for hepatitis C. In spite of its success in controlling hepatitis C infection, it has also been associated with treatment-related adverse side effects. The most common and life threatening among them is hemolytic anemia, necessitating dose reduction or therapy cessation.

Sharpness of saturation in harvesting and predation.

Harvesting and predation occur through contact processes in which the rate at which the managed (prey) population can be found depends on the population size, usually saturating at high densities. Many models incorporate saturation in this process without considering the effects of the particular function used to describe it. We show that the sharpness with which this saturation occurs has an important effect upon the resulting population dynamics, with bistability (sometimes involving a stable equilibrium and a stable limit cycle) occurring for saturation that is any sharper than the commonly used Michaelis-Menten (Holling type II) functional response.

Transmission dynamics and underreporting of Kala-azar in the Indian state of Bihar.

"Kala-azar" (or Indian Visceral Leishmaniasis) is a vector-borne infectious disease affecting communities in tropical and subtropical areas of the world. Bihar, a state in India, has one of the highest prevalence and mortality reported levels of Kala-azar. Yet, the magnitude of the problem is difficult to assess because most cases are handled by private health providers who are not required to and do not report them to the Ministry of Health.

The effect of the hiv/aids epidemic on africa's truck drivers.

The AIDS epidemic is having a growing impact on the transport sector of the economy of sub-Saharan Africa, where long-distance truck drivers are at an increased risk of infection due to their frequent contacts with commercial sex workers. The spread of AIDS in the transport industry is especially significant to the economy, as truck drivers are largely responsible for transporting crops and supplies needed for daily subsistence. In this paper we analyze these effects via two models, one employing a switch and the other a Verhulst saturation function, to describe the rate at which new drivers are recruited in terms of the supply and demand for them in the general population.

To switch or taper off: the dynamics of saturation.

Many situations in population biology involve a rate--typically a contact or recruitment rate--which increases linearly for small populations but reaches a maximum value (saturates) for large populations. Models for populations of variable size need to incorporate both characteristics to predict behavior accurately. This can be done by defining the rate as a continuous, piecewise linear function with a switch point, or via a Verhulst-type (smooth) saturation function.

Model parameters and outbreak control for SARS.

Control of the 2002-2003 severe acute respiratory syndrome (SARS) outbreak was based on rapid diagnosis coupled with effective patient isolation. We used uncertainty and sensitivity analysis of the basic reproductive number R0 to assess the role that model parameters play in outbreak control. The transmission rate and isolation effectiveness have the largest fractional effect on R0.

Effects of education, vaccination and treatment on HIV transmission in homosexuals with genetic heterogeneity.

Genetic studies report the existence of a mutant allele Delta32 of CCR5 chemokine receptor gene at high allele frequencies (approximately 10%) in Caucasian populations. The presence of this allele is believed to provide partial or full resistance to HIV. In this study, we look at the impact of education, temporarily effective vaccines and therapies on the dynamics of HIV in homosexually active populations.

Vaccination strategies and backward bifurcation in an age-since-infection structured model.

We consider models for a disease with acute and chronic infective stages, and variable infectivity and recovery rates, within the context of a vaccination campaign. Models for SIRS and SIS disease cycles exhibit backward bifurcations under certain conditions, which complicate the criteria for success of the vaccination campaign by making it possible to have stable endemic states when R(0)<1. We also show the extent to which the forms of the infectivity and recovery functions affect the possibility of backward bifurcations.