A key question in pandemic influenza is the relative roles of innate immunity and target cell depletion in limiting primary infection and modulating pathology. Here, we model these interactions using detailed data from equine influenza virus infection, combining viral and immune (type I interferon) kinetics with estimates of cell depletion. The resulting dynamics indicate a powerful role for innate immunity in controlling the rapid peak in virus shedding. As a corollary, cells are much less depleted than suggested by a model of human influenza based only on virus-shedding data. We then explore how differences in the influence of viral proteins on interferon kinetics can account for the observed spectrum of virus shedding, immune response, and influenza pathology. In particular, induction of high levels of interferon ("cytokine storms"), coupled with evasion of its effects, could lead to severe pathology, as hypothesized for some fatal cases of influenza.

Influenza pandemics occur when a novel influenza strain, often of animal origin, becomes transmissible between humans. Domestic animal species such as poultry or swine in confined animal feeding operations (CAFOs) could serve as local amplifiers for such a new strain of influenza. A mathematical model is used to examine the transmission dynamics of a new influenza virus among three sequentially linked populations: the CAFO species, the CAFO workers (the bridging population), and the rest of the local human population. Using parameters based on swine data, simulations showed that when CAFO workers comprised 15-45% of the community, human influenza cases increased by 42-86%. Successful vaccination of at least 50% of CAFO workers cancelled the amplification. A human influenza epidemic due to a new virus could be locally amplified by the presence of confined animal feeding operations in the community. Thus vaccination of CAFO workers would be an effective use of a pandemic vaccine.

Primary schools constitute a key risk group for the transmission of infectious diseases, concentrating great numbers of immunologically naive individuals at high densities. Despite this, very little is known about the social patterns of mixing within a school, which are likely to contribute to disease transmission. In this study, we present a novel approach where scientific engagement was used as a tool to access school populations and measure social networks between young (4–11 years) children. By embedding our research project within enrichment activities to older secondary school (13–15) children, we could exploit the existing links between schools to achieve a high response rate for our study population (around 90% in most schools). Social contacts of primary school children were measured through self-reporting based on a questionnaire design, and analysed using the techniques of social network analysis. We find evidence of marked social structure and gender assortativity within and between classrooms in the same school. These patterns have been previously reported in smaller studies, but to our knowledge no study has attempted to exhaustively sample entire school populations. Our innovative approach facilitates access to a vitally important (but difficult to sample) epidemiological sub-group. It provides a model whereby scientific communication can be used to enhance, rather than merely complement, the outcomes of research.

We develop a simple method to obtain approximate analytical expressions for the period of a particle moving in a given potential. The method is inspired to the Linear Delta Expansion (LDE) and it is applied to a large class of potentials. Precise formulas for the period are obtained. PACS numbers: 45.10.Db, In this letter we consider the problem of calculating the period of a unit mass moving in a potential V (x). Although it is possible to solve this problem analytically only in a few cases, depending upon the form of the potential, several methods to find approximate results have been devised in the past. Many of the techniques that are used to solve this kind of problems are based on a perturbative expansion in some small parameter that appears in the equations of motion. This is the case of the Lindstedt-Poincaré method and of the multiple-scale method. Unfortunately the validity of these approaches is restricted to the domain of weak couplings and the series obtained rapidly diverge when larger couplings are considered. Recently, one of the authors and collaborators devised a non-perturbative version of the LindstedtPoincaré method, based on the ideas of the Linear Delta Expansion (LDE) [1], which allows to obtain very accurate results in a wide class of non linear problems [2,3,4]. In this letter we propose a different method, also inspired by the LDE, whose application is much simpler and for which convergence to the exact result can be proven.Let us describe the method in detail. We consider a unit mass moving in a potential V (x). The total energy E =ẋ 2 2 +V (x) is conserved during the motion. The exact period of the oscillations will be given by:where x ± are the inversion points, obtained by solving the equation E = V (x ± ). Only in few cases it is possible to evaluate the integral (1) analytically. In the spirit of the Linear Delta Expansion (LDE) we interpolate the full potential V (x) with a solvable oneWe want to perform this interpolation without moving the inversion points; for this reason we ask that x ± be the inversion points also of the potential V 0 (x). As a 1 By solvable here we mean that the integralresult, the energy E 0 that the particle would possess if it was moving only in the potential V 0 (x) will be given byWe are now in position to rewrite eq. (1) asWe notice that Eq. (2) reduces to Eq. (1) for δ = 1; for δ = 0 this formula yields the period of oscillation between the points x ± in the potential V 0 (x). We will treat the term proportional to δ as a perturbation and expand in powers of δ. Since V 0 (x) depends upon one or more arbitrary parameters (which we will indicate with λ) a residual dependence upon these parameters shows up in the period when the expansion is carried out to a finite order. In order to eliminate such unnatural dependence we impose the Principle of Minimal Sensitivity (PMS) [5] by requiring that ∂T ∂λ = 0.Finally, we can write explicitly the period by performing an expansion in δ and obtain

In 1988 the first author and J. A. Guthrie published a theorem which characterizes the topological structure of the set of subsums of an infinite series. In 1998, while attempting to generalize this result, the second author noticed the proof of the original theorem was not complete and perhaps not correct. The present paper presents a complete and correct proof of this theorem.

Outbreaks of avian influenza in poultry can be devastating, yet many of the basic epidemiological parameters have not been accurately characterised. In 1999–2000 in Northern Italy, outbreaks of H7N1 low pathogenicity avian influenza virus (LPAI) were followed by the emergence of H7N1 highly pathogenic avian influenza virus (HPAI). This study investigates the transmission dynamics in turkeys of representative HPAI and LPAI H7N1 virus strains from this outbreak in an experimental setting, allowing direct comparison of the two strains. The fitted transmission rates for the two strains are similar: 2.04 (1.5–2.7) per day for HPAI, 2.01 (1.6–2.5) per day for LPAI. However, the mean infectious period is far shorter for HPAI (1.47 (1.3–1.7) days) than for LPAI (7.65 (7.0–8.3) days), due to the rapid death of infected turkeys. Hence the basic reproductive ratio, is significantly lower for HPAI (3.01 (2.2–4.0)) than for LPAI (15.3 (11.8–19.7)). The comparison of transmission rates and are critically important in relation to understanding how HPAI might emerge from LPAI. Two competing hypotheses for how transmission rates vary with population size are tested by fitting competing models to experiments with differing numbers of turkeys. A model with frequency-dependent transmission gives a significantly better fit to experimental data than density-dependent transmission. This has important implications for extrapolating experimental results from relatively small numbers of birds to the commercial poultry flock size, and for how control, including vaccination, might scale with flock size.

In this paper we generalize and improve a method for calculating the period of a classical oscillator and other integrals of physical interest, which was recently developed by some of the authors. We derive analytical expressions that prove to be more accurate than those commonly found in the literature, and test the convergence of the series produced by the approach.

The use of antiretroviral therapy (ART) is the most efficient measure in controlling the HIV epidemic. However, emergence of drug-resistant strains can reduce the potential benefits of ART. The viral dynamics of drug-sensitive and drug-resistant strains at the individual level may play a crucial role in the emergence and spread of drug resistance in a population. We investigate the effect of the viral dynamics within an infected individual on the epidemiological dynamics of HIV using a nested model that links both dynamical levels. A time-dependent between-host transmission rate that receives feedback from a model of two-strain virus dynamics within a host is incorporated into an epidemiological model of HIV. We analyze the resulting dynamics of the model and identify model parameters such as time when ART is initiated, fraction of cases treated, and the probability that a patient develops drug resistance, as having the greatest impact on total infection and prevalence of drug resistance. Importantly, for small values of the risk of a patient developing drug resistance, increasing the fraction of cases treated can increase the cumulative number of infected individuals. Such a pattern is the result of the balance between not treating a patient and having future cases still sensitive to treatment, and treating the patient and increasing the chances for future (untreatable) drug-resistant infections. The current modeling framework incorporates important aspects of virus dynamics within a host into an epidemic model. This approach provides useful insights on the drug resistance dynamics of an epidemic of HIV, which may assist in identifying an optimal use of ART.