Theoretical basis to measure the impact of short-lasting control of an infectious disease on the epidemic peak

Background. While many pandemic preparedness plans have promoted disease control effort to lower and delay an epidemic peak, analytical methods for determining the required control effort and making statistical inferences have yet to be sought. As a first step to address this issue, we present a theoretical basis on which to assess the impact of an early intervention on the epidemic peak, employing a simple epidemic model. Methods. We focus on estimating the impact of an early control effort (e.g. unsuccessful containment), assuming that the transmission rate abruptly increases when control is discontinued. We provide analytical expressions for magnitude and time of the epidemic peak, employing approximate logistic and logarithmic-form solutions for the latter. Empirical influenza data (H1N1-2009) in Japan are analyzed to estimate the effect of the summer holiday period in lowering and delaying the peak in 2009. Results. Our model estimates that the epidemic peak of the 2009 pandemic was delayed for 21 days due to summer holiday. Decline in peak appears to be a nonlinear function of control-associated reduction in the reproduction number. Peak delay is shown to critically depend on the fraction of initially immune individuals. Conclusions. The proposed modeling approaches offer methodological avenues to assess empirical data and to objectively estimate required control effort to lower and delay an epidemic peak. Analytical findings support a critical need to conduct population-wide serological survey as a prior requirement for estimating the time of peak. © 2011 Omori and Nishiura; licensee BioMed Central Ltd.published_or_final_versio

Two-parameter neutrino mass matrices with two texture zeros

We reanalyse Majorana-neutrino mass matrices M_nu with two texture zeros, by searching for viable hybrid textures in which the non-zero matrix elements of M_nu have simple ratios. Referring to the classification scheme of Frampton, Glashow and Marfatia, we find that the mass matrix denoted by A1 allows the ratios (M_nu)_{mu mu} : (Mnu)_{tau tau} = 1:1 and (M_nu)_{e tau} : (Mnu)_{mu tau} = 1:2. There are analogous ratios for texture A2. With these two hybrid textures, one obtains, for instance, good agreement with the data if one computes the three mixing angles in terms of the experimentally determined mass-squared differences Delta m^2_21 and Delta m^2_31. We could not find viable hybrid textures based on mass matrices different from those of cases A1 and A2.Comment: 10 pages, no figures, minor changes, some references adde

Dengue disease, basic reproduction number and control

Dengue is one of the major international public health concerns. Although progress is underway, developing a vaccine against the disease is challenging. Thus, the main approach to fight the disease is vector control. A model for the transmission of Dengue disease is presented. It consists of eight mutually exclusive compartments representing the human and vector dynamics. It also includes a control parameter (insecticide) in order to fight the mosquito. The model presents three possible equilibria: two disease-free equilibria (DFE) and another endemic equilibrium. It has been proved that a DFE is locally asymptotically stable, whenever a certain epidemiological threshold, known as the basic reproduction number, is less than one. We show that if we apply a minimum level of insecticide, it is possible to maintain the basic reproduction number below unity. A case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented.Comment: This is a preprint of a paper whose final and definitive form has appeared in International Journal of Computer Mathematics (2011), DOI: 10.1080/00207160.2011.55454

Reaction-Diffusion System in a Vesicle with Semi-Permeable Membrane

We study the Schloegl model in a vesicle with semi-permeable membrane. The diffusion constant takes a smaller value in the membrane region, which prevents the outflow of self-catalytic product. A nonequilibrium state is stably maintained inside of the vesicle. Nutrients are absorbed and waste materials are exhausted through the membrane by diffusion. It is interpreted as a model of primitive metabolism in a cell.Comment: 8 pages, 6 figure

Pros and cons of estimating the reproduction number from early epidemic growth rate of influenza A (H1N1) 2009

<p>Abstract</p> <p>Background</p> <p>In many parts of the world, the exponential growth rate of infections during the initial epidemic phase has been used to make statistical inferences on the reproduction number, <it>R</it>, a summary measure of the transmission potential for the novel influenza A (H1N1) 2009. The growth rate at the initial stage of the epidemic in Japan led to estimates for <it>R </it>in the range 2.0 to 2.6, capturing the intensity of the initial outbreak among school-age children in May 2009.</p> <p>Methods</p> <p>An updated estimate of <it>R </it>that takes into account the epidemic data from 29 May to 14 July is provided. An age-structured renewal process is employed to capture the age-dependent transmission dynamics, jointly estimating the reproduction number, the age-dependent susceptibility and the relative contribution of imported cases to secondary transmission. Pitfalls in estimating epidemic growth rates are identified and used for scrutinizing and re-assessing the results of our earlier estimate of <it>R</it>.</p> <p>Results</p> <p>Maximum likelihood estimates of <it>R </it>using the data from 29 May to 14 July ranged from 1.21 to 1.35. The next-generation matrix, based on our age-structured model, predicts that only 17.5% of the population will experience infection by the end of the first pandemic wave. Our earlier estimate of <it>R </it>did not fully capture the population-wide epidemic in quantifying the next-generation matrix from the estimated growth rate during the initial stage of the pandemic in Japan.</p> <p>Conclusions</p> <p>In order to quantify <it>R </it>from the growth rate of cases, it is essential that the selected model captures the underlying transmission dynamics embedded in the data. Exploring additional epidemiological information will be useful for assessing the temporal dynamics. Although the simple concept of <it>R </it>is more easily grasped by the general public than that of the next-generation matrix, the matrix incorporating detailed information (e.g., age-specificity) is essential for reducing the levels of uncertainty in predictions and for assisting public health policymaking. Model-based prediction and policymaking are best described by sharing fundamental notions of heterogeneous risks of infection and death with non-experts to avoid potential confusion and/or possible misuse of modelling results.</p

Optical Versus Mid-Infrared Spectroscopic Classification of Ultraluminous Infrared Galaxies

The origin of huge infrared luminosities of ultraluminous infrared galaxies (ULIGs) is still in question. Recently, Genzel et al. made mid-infrared (MIR) spectroscopy of a large number of ULIGs and found that the major energy source in them is massive stars formed in the recent starburst activity; i.e., $\sim$ 70% -- 80% of the sample are predominantly powered by the starburst. However, it is known that previous optical spectroscopic observations showed that the majority of ULIGs are classified as Seyferts or LINERs (low-ionization nuclear emission-line regions). In order to reconcile this difference, we compare types of emission-line activity for a sample of ULIGs which have been observed in both optical and MIR. We confirm the results of previous studies that the majority of ULIGs classified as LINERs based on the optical emission-line diagnostics turn to be starburst-dominated galaxies based on the MIR ones. Since the MIR spectroscopy can probe more heavily-reddened, inner parts of the ULIGs, it is quite unlikely that the inner parts are powered by the starburst while the outer parts are powered by non-stellar ionization sources. The most probable resolution of this dilemma is that the optical emission-line nebulae with the LINER properties are powered predominantly by shock heating driven by the superwind activity; i.e., a blast wave driven by a collective effect of a large number of supernovae in the central region of galaxy mergers.Comment: 15 pages, 2 tables, and 3 eps figures. The Astrophysical Journal (Part 1), in pres

A three-parameter model for the neutrino mass matrix

Using the type-II seesaw mechanism with three Higgs doublets phi_alpha (alpha = e, mu, tau) and four Higgs triplets, we build a model for lepton mixing based on a 384-element horizontal symmetry group, generated by the permutation group S_3 and by six Z_2 transformations. The charged-lepton mass matrix is diagonal; the symmetries of the model would require all the three masses m_alpha to be equal, but different vacuum expectation values of the phi_alpha allow the m_alpha to split. The number of parameters in the Majorana neutrino mass matrix m_nu depends on two options: full breaking of the permutation group S_3, or leaving a mu--tau interchange symmetry intact; and hard or spontaneous violation of CP. We discuss in detail the case with the minimal number of three parameters, wherein m_nu is real, symmetric under mu--tau interchange, and has equal diagonal elements. In that case, CP is conserved in lepton mixing, atmospheric neutrino mixing is maximal, and theta_{13} = 0; moreover, the type of neutrino mass spectrum and the absolute neutrino mass scale are sensitive functions of the solar mixing angle.Comment: 16 pages, one eps figure; some clarifications added, contains new section 5, version accepted for publication in J. Phys.

Extracting key information from historical data to quantify the transmission dynamics of smallpox

<p>Abstract</p> <p>Background</p> <p>Quantification of the transmission dynamics of smallpox is crucial for optimizing intervention strategies in the event of a bioterrorist attack. This article reviews basic methods and findings in mathematical and statistical studies of smallpox which estimate key transmission parameters from historical data.</p> <p>Main findings</p> <p>First, critically important aspects in extracting key information from historical data are briefly summarized. We mention different sources of heterogeneity and potential pitfalls in utilizing historical records. Second, we discuss how smallpox spreads in the absence of interventions and how the optimal timing of quarantine and isolation measures can be determined. Case studies demonstrate the following. (1) The upper confidence limit of the 99th percentile of the incubation period is 22.2 days, suggesting that quarantine should last 23 days. (2) The highest frequency (61.8%) of secondary transmissions occurs 3–5 days after onset of fever so that infected individuals should be isolated before the appearance of rash. (3) The U-shaped age-specific case fatality implies a vulnerability of infants and elderly among non-immune individuals. Estimates of the transmission potential are subsequently reviewed, followed by an assessment of vaccination effects and of the expected effectiveness of interventions.</p> <p>Conclusion</p> <p>Current debates on bio-terrorism preparedness indicate that public health decision making must account for the complex interplay and balance between vaccination strategies and other public health measures (e.g. case isolation and contact tracing) taking into account the frequency of adverse events to vaccination. In this review, we summarize what has already been clarified and point out needs to analyze previous smallpox outbreaks systematically.</p

Hermitian quark mass matrices with four texture zeros

We provide a complete and systematic analysis of hermitian, hierarchical quark mass matrices with four texture zeros. Using triangular mass matrices, each pattern of texture zeros is readily shown to lead to a definite relation between the CKM parameters and the quark masses. Nineteen pairs are found to be consistent with present data, and one other is marginally acceptable. In particular, no parallel structure between the up and down mass matrices is found to be favorable with data.Comment: 18 pages, no figure, references [8] and [10] adde

Epidemiological and transmissibility analysis of influenza A(H1N1)v in a southern hemisphere setting: Peru

We present a preliminary analysis of 1,771 confirmed cases of influenza A(H1N1)v reported in Peru by 17 July including the frequency of the clinical characteristics, the spatial and age distribution of the cases and the estimate of the transmission potential. Age-specific frequency of cases was highest among school age children and young adults, with the lowest frequency of cases among seniors, a pattern that is consistent with reports from other countries. Estimates of the reproduction number lie in the range of 1.2 to 1.7, which is broadly consistent with previous estimates for this pandemic in other regions. Validation of these estimates will be possible as additional data become available