Appropriate models for the management of infectious diseases

Background Mathematical models have become invaluable management tools for epidemiologists, both shedding light on the mechanisms underlying observed dynamics as well as making quantitative predictions on the effectiveness of different control measures. Here, we explain how substantial biases are introduced by two important, yet largely ignored, assumptions at the core of the vast majority of such models. Methods and Findings First, we use analytical methods to show that (i) ignoring the latent period or (ii) making the common assumption of exponentially distributed latent and infectious periods (when including the latent period) always results in underestimating the basic reproductive ratio of an infection from outbreak data. We then proceed to illustrate these points by fitting epidemic models to data from an influenza outbreak. Finally, we document how such unrealistic a priori assumptions concerning model structure give rise to systematically overoptimistic predictions on the outcome of potential management options. Conclusion This work aims to highlight that, when developing models for public health use, we need to pay careful attention to the intrinsic assumptions embedded within classical frameworks

Absorption, Photoluminescence and Resonant Rayleigh Scattering Probes of Condensed Microcavity Polaritons

We investigate and compare different optical probes of a condensed state of microcavity polaritons in expected experimental conditions of non-resonant pumping. We show that the energy- and momentum-resolved resonant Rayleigh signal provide a distinctive probe of condensation as compared to, e.g., photoluminescence emission. In particular, the presence of a collective sound mode both above and below the chemical potential can be observed, as well as features directly related to the density of states of particle-hole like excitations. Both resonant Rayleigh response and the absorption and photoluminescence, are affected by the presence of quantum well disorder, which introduces a distribution of oscillator strengths between quantum well excitons at a given energy and cavity photons at a given momentum. As we show, this distribution makes it important that in the condensed regime, scattering by disorder is taken into account to all orders. We show that, in the low density linear limit, this approach correctly describes inhomogeneous broadening of polaritons. In addition, in this limit, we extract a linear blue-shift of the lower polariton versus density, with a coefficient determined by temperature and by a characteristic disorder length.Comment: 16 pages, 11 figures; minor correction

Non-equilibrium quantum condensation in an incoherently pumped dissipative system

We study spontaneous quantum coherence in an out of equilibrium system, coupled to multiple baths describing pumping and decay. For a range of parameters describing coupling to, and occupation of the baths, a stable steady-state condensed solution exists. The presence of pumping and decay significantly modifies the spectra of phase fluctuations, leading to correlation functions that differ both from an isolated condensate and from a laser.Comment: 5 pages, 2 eps figure

Topographic determinants of foot and mouth disease transmission in the UK 2001 epidemic

Background A key challenge for modelling infectious disease dynamics is to understand the spatial spread of infection in real landscapes. This ideally requires a parallel record of spatial epidemic spread and a detailed map of susceptible host density along with relevant transport links and geographical features. Results Here we analyse the most detailed such data to date arising from the UK 2001 foot and mouth epidemic. We show that Euclidean distance between infectious and susceptible premises is a better predictor of transmission risk than shortest and quickest routes via road, except where major geographical features intervene. Conclusion Thus, a simple spatial transmission kernel based on Euclidean distance suffices in most regions, probably reflecting the multiplicity of transmission routes during the epidemic

Thermodynamics and Excitations of Condensed Polaritons in Disordered Microcavities

We study the thermodynamic condensation of microcavity polaritons using a realistic model of disorder in semiconductor quantum wells. This approach correctly describes the polariton inhomogeneous broadening in the low density limit, and treats scattering by disorder to all orders in the condensed regime. While the weak disorder changes the thermodynamic properties of the transition little, the effects of disorder in the condensed state are prominent in the excitations and can be seen in resonant Rayleigh scattering.Comment: 5 pages, 3 eps figures (published version

A motif-based approach to network epidemics

Networks have become an indispensable tool in modelling infectious diseases, with the structure of epidemiologically relevant contacts known to affect both the dynamics of the infection process and the efficacy of intervention strategies. One of the key reasons for this is the presence of clustering in contact networks, which is typically analysed in terms of prevalence of triangles in the network. We present a more general approach, based on the prevalence of different four-motifs, in the context of ODE approximations to network dynamics. This is shown to outperform existing models for a range of small world networks

Bath induced coherence and the secular approximation

Finding efficient descriptions of how an environment affects a collection of discrete quantum systems would lead to new insights into many areas of modern physics. Markovian, or time-local, methods work well for individual systems, but for groups a question arises: does system-bath or inter-system coupling dominate the dissipative dynamics? The answer has profound consequences for the long-time quantum correlations within the system. We consider two bosonic modes coupled to a bath. By comparing an exact solution to different Markovian master equations, we find that a smooth crossover of the equations-of-motion between dominant inter-system and system-bath coupling exists - but requires a non-secular master equation. We predict a singular behaviour of the dynamics, and show that the ultimate failure of non-secular equations of motion is essentially a failure of the Markov approximation. Our findings justify the use of time-local theories throughout the crossover between system-bath dominated and inter-system-coupling dominated dynamics.PostprintPeer reviewe

Angular distribution of photoluminescence as a probe of Bose Condensation of trapped excitons

Recent experiments on two-dimensional exciton systems have shown the excitons collect in shallow in-plane traps. We find that Bose condensation in a trap results in a dramatic change of the exciton photoluminescence (PL) angular distribution. The long-range coherence of the condensed state gives rise to a sharply focussed peak of radiation in the direction normal to the plane. By comparing the PL profile with and without Bose Condensation we provide a simple diagnostic for the existence of a Bose condensate. The PL peak has strong temperature dependence due to the thermal order parameter phase fluctuations across the system. The angular PL distribution can also be used for imaging vortices in the trapped condensate. Vortex phase spatial variation leads to destructive interference of PL radiation in certain directions, creating nodes in the PL distribution that imprint the vortex configuration.Comment: 4 pages, 3 figure

A change of IL-2 and IL-4 production in patients with Helicobactor pylori infection

Hellcobacter pylori is the most common cause of gastroduodenal inflammation. However, the exact immune pathogenesis is not fully understood. To look for evidence of the immunological mechanism in H. pylori associated disease, we measured cytokine interleukin-2 (IL-2) and IL-4 levels produced by peripheral blood lymphocytes (PBL) and gastric biopsies in 20 subjects with or without H. pylori infection. H. pylori can stimulate IL-2 and IL-4 production from PBL in H. pylori negative as well as H. pylori positive individuals. The spontaneous IL-2 production by PBL and gastric biopsies was greater (p < 0.0025, <0.001)in H. pylori negative individuals than that in H. pylori infected patients. Increased IL-4 levels from PBL in H. pylori infected patients were found in the presence of H. pylori (p < 0.0025). An increased spontaneous production of IL-4 from gastric biopsies was also observed in H. pylori infected patients (p < 0.025). In conclusion, an enhanced type 2 cytokine production was observed in H. pylori infected patients, which may be responsible for H. pylori chronic infection

Performance of an environmental test to detect Mycobacterium bovis infection in badger social groups

A study by Courtenay and others (2006) demonstrated that the probability of detecting Mycobacterium bovis by PCR in soil samples from the spoil heaps of main badger setts correlated with the prevalence of excretion (infectiousness) of captured badgers belonging to the social group. It has been proposed that such a test could be used to target badger culling to setts containing infectious animals (Anon 2007). This short communication discusses the issues surrounding this concept, with the intention of dispelling any misconceptions among relevant stakeholders (farmers, policy makers and conservationists)