Analysis of symmetries in models of multi-strain infections

In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with cross-immunity between strains, we show that a significant understanding of the stability of steady states and possible dynamical behaviours can be achieved when the symmetry of interactions between strains is taken into account. Techniques of equivariant bifurcation theory allow one to identify the type of possible symmetry-breaking Hopf bifurcation, as well as to classify different periodic solutions in terms of their spatial and temporal symmetries. The approach is also illustrated on other models of multi-strain diseases, where the same methodology provides a systematic understanding of bifurcation scenarios and periodic behaviours. The results of the analysis are quite generic, and have wider implications for understanding the dynamics of a large class of models of multi-strain diseases

The effects of symmetry on the dynamics of antigenic variation

In the studies of dynamics of pathogens and their interactions with a host immune system, an important role is played by the structure of antigenic variants associated with a pathogen. Using the example of a model of antigenic variation in malaria, we show how many of the observed dynamical regimes can be explained in terms of the symmetry of interactions between different antigenic variants. The results of this analysis are quite generic, and have wider implications for understanding the dynamics of immune escape of other parasites, as well as for the dynamics of multi-strain diseases.Comment: 21 pages, 4 figures; J. Math. Biol. (2012), Online Firs

Continuation for thin film hydrodynamics and related scalar problems

This chapter illustrates how to apply continuation techniques in the analysis of a particular class of nonlinear kinetic equations that describe the time evolution through transport equations for a single scalar field like a densities or interface profiles of various types. We first systematically introduce these equations as gradient dynamics combining mass-conserving and nonmass-conserving fluxes followed by a discussion of nonvariational amendmends and a brief introduction to their analysis by numerical continuation. The approach is first applied to a number of common examples of variational equations, namely, Allen-Cahn- and Cahn-Hilliard-type equations including certain thin-film equations for partially wetting liquids on homogeneous and heterogeneous substrates as well as Swift-Hohenberg and Phase-Field-Crystal equations. Second we consider nonvariational examples as the Kuramoto-Sivashinsky equation, convective Allen-Cahn and Cahn-Hilliard equations and thin-film equations describing stationary sliding drops and a transversal front instability in a dip-coating. Through the different examples we illustrate how to employ the numerical tools provided by the packages auto07p and pde2path to determine steady, stationary and time-periodic solutions in one and two dimensions and the resulting bifurcation diagrams. The incorporation of boundary conditions and integral side conditions is also discussed as well as problem-specific implementation issues

Influenza A Gradual and Epochal Evolution: Insights from Simple Models

The recurrence of influenza A epidemics has originally been explained by a “continuous antigenic drift” scenario. Recently, it has been shown that if genetic drift is gradual, the evolution of influenza A main antigen, the haemagglutinin, is punctuated. As a consequence, it has been suggested that influenza A dynamics at the population level should be approximated by a serial model. Here, simple models are used to test whether a serial model requires gradual antigenic drift within groups of strains with the same antigenic properties (antigenic clusters). We compare the effect of status based and history based frameworks and the influence of reduced susceptibility and infectivity assumptions on the transient dynamics of antigenic clusters. Our results reveal that the replacement of a resident antigenic cluster by a mutant cluster, as observed in data, is reproduced only by the status based model integrating the reduced infectivity assumption. This combination of assumptions is useful to overcome the otherwise extremely high model dimensionality of models incorporating many strains, but relies on a biological hypothesis not obviously satisfied. Our findings finally suggest the dynamical importance of gradual antigenic drift even in the presence of punctuated immune escape. A more regular renewal of susceptible pool than the one implemented in a serial model should be part of a minimal theory for influenza at the population level

Do physician outcome judgments and judgment biases contribute to inappropriate use of treatments? Study protocol

<p>Abstract</p> <p>Background</p> <p>There are many examples of physicians using treatments inappropriately, despite clear evidence about the circumstances under which the benefits of such treatments outweigh their harms. When such over- or under- use of treatments occurs for common diseases, the burden to the healthcare system and risks to patients can be substantial. We propose that a major contributor to inappropriate treatment may be how clinicians judge the likelihood of important treatment outcomes, and how these judgments influence their treatment decisions. The current study will examine the role of judged outcome probabilities and other cognitive factors in the context of two clinical treatment decisions: 1) prescription of antibiotics for sore throat, where we hypothesize overestimation of benefit and underestimation of harm leads to over-prescription of antibiotics; and 2) initiation of anticoagulation for patients with atrial fibrillation (AF), where we hypothesize that underestimation of benefit and overestimation of harm leads to under-prescription of warfarin.</p> <p>Methods</p> <p>For each of the two conditions, we will administer surveys of two types (Type 1 and Type 2) to different samples of Canadian physicians. The primary goal of the Type 1 survey is to assess physicians' perceived outcome probabilities (both good and bad outcomes) for the target treatment. Type 1 surveys will assess judged outcome probabilities in the context of a representative patient, and include questions about how physicians currently treat such cases, the recollection of rare or vivid outcomes, as well as practice and demographic details. The primary goal of the Type 2 surveys is to measure the specific factors that drive individual clinical judgments and treatment decisions, using a 'clinical judgment analysis' or 'lens modeling' approach. This survey will manipulate eight clinical variables across a series of sixteen realistic case vignettes. Based on the survey responses, we will be able to identify which variables have the greatest effect on physician judgments, and whether judgments are affected by inappropriate cues or incorrect weighting of appropriate cues. We will send antibiotics surveys to family physicians (300 per survey), and warfarin surveys to both family physicians and internal medicine specialists (300 per group per survey), for a total of 1,800 physicians. Each Type 1 survey will be two to four pages in length and take about fifteen minutes to complete, while each Type 2 survey will be eight to ten pages in length and take about thirty minutes to complete.</p> <p>Discussion</p> <p>This work will provide insight into the extent to which clinicians' judgments about the likelihood of important treatment outcomes explain inappropriate treatment decisions. This work will also provide information necessary for the development of an individualized feedback tool designed to improve treatment decisions. The techniques developed here have the potential to be applicable to a wide range of clinical areas where inappropriate utilization stems from biased judgments.</p

Exploiting Fast-Variables to Understand Population Dynamics and Evolution

We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are caused by individual events while the dynamics are described in terms of the time-evolution of a probability density function. In general, the application of the diffusion approximation still leaves a description that is quite complex. However, in many biological applications one or more of the processes happen slowly relative to the system's other processes, and the dynamics can be approximated as occurring within a slow low-dimensional subspace. We review these time-scale separation arguments and analyse the more simple stochastic dynamics that result in a number of cases. We stress that it is important to retain the demographic noise derived in this way, and emphasise this point by showing that it can alter the direction of selection compared to the prediction made from an analysis of the corresponding deterministic model.Comment: 33 pages, 9 figure