Household epidemic models with varying infection response

This paper is concerned with SIR (susceptible $\to$ infected $\to$ removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an individual. Two different models are analysed. In the first model, the infection status of an individual is predetermined, perhaps due to partial immunity, and in the second, the infection status of an individual depends on the infection status of its infector and on whether the individual was infected by a within- or between-household contact. The first scenario may be modelled using a multitype household epidemic model, and the second scenario by a model we denote by the infector-dependent-severity household epidemic model. Large population results of the two models are derived, with the focus being on the distribution of the total numbers of mild and severe cases in a typical household, of any given size, in the event that the epidemic becomes established. The aim of the paper is to investigate whether it is possible to determine which of the two underlying explanations is causing the varying response when given final size household outbreak data containing mild and severe cases. We conduct numerical studies which show that, given data on sufficiently many households, it is generally possible to discriminate between the two models by comparing the Kullback-Leibler divergence for the two fitted models to these data.Comment: 29 pages; submitted to Journal of Mathematical Biolog

Epidemics on random intersection graphs

In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of cliques, each of random size, and infection can be transmitted between two individuals if and only if there is a clique they both belong to. Both the clique sizes and the number of cliques an individual belongs to follow mixed Poisson distributions. An infinite-type branching process approximation (with type being given by the length of an individual's infectious period) for the early stages of an epidemic is developed and made fully rigorous by proving an associated limit theorem as the population size tends to infinity. This leads to a threshold parameter $R_*$, so that in a large population an epidemic with few initial infectives can give rise to a large outbreak if and only if $R_*>1$. A functional equation for the survival probability of the approximating infinite-type branching process is determined; if $R_*\le1$, this equation has no nonzero solution, while if $R_*>1$, it is shown to have precisely one nonzero solution. A law of large numbers for the size of such a large outbreak is proved by exploiting a single-type branching process that approximates the size of the susceptibility set of a typical individual.Comment: Published in at http://dx.doi.org/10.1214/13-AAP942 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

The evaluation of an active networking approach for supporting the QOS requirements of distributed virtual environments

This paper describes work that is part of a more general investigation into how Active Network ideas might benefit large scale Distributed-Virtual-Environments (DVEs). Active Network approaches have been shown to offer improved solutions to the Scalable Reliable Multicast problem, and this is in a sense the lowest level at which Active Networks might benefit DVEs in supporting the peer-to-peer architectures considered most promising for large scale DVEs. To go further than this, the key benefit of Active Networking is the ability to take away from the application the need to understand the network topology and delegate the execution of certain actions, for example intelligent message pruning, to the network itself. The need to exchange geometrical information results in a type of traffic that can place occasional, short-lived, but heavy loads on the network. However, the Level of Detail (LoD) concept provides the potential to reduce this loading in certain circumstances. This paper introduces the performance modelling approach being used to evaluate the effectiveness of active network approaches for supporting DVEs and presents an evaluation of messages filtering mechanisms, which are based on the (LoD) concept. It describes the simulation experiment used to carry out the evaluation, presents its results and discusses plans for future work

Oral History Interview: Frank Ball

In this interview, Frank Ball discusses the history of Barboursville and West Virginia, including the Civil War, slavery, religion, railroads, specific people who lived in the area, Jesse James. and events from the 1800\u27s. This interview is one of series conducted concerning the Oral History of Appalachia.https://mds.marshall.edu/oral_history/1211/thumbnail.jp

Household epidemic models with varying infection response

This paper is concerned with SIR (susceptible--infected--removed) household epidemic models in which the infection response may be either mild or severe, with the type of response also affecting the infectiousness of an individual. Two different models are analysed. In the first model, the infection status of an individual is predetermined, perhaps due to partial immunity, and in the second, the infection status of an individual depends on the infection status of its infector and on whether the individual was infected by a within- or between-household contact. The first scenario may be modelled using a multitype household epidemic model, and the second scenario by a model we denote by the infector-dependent-severity household epidemic model. Large population results of the two models are derived, with the focus being on the distribution of the total numbers of mild and severe cases in a typical household, of any given size, in the event that the epidemic becomes established. The aim of the paper is to investigate whether it is possible to determine which of the two underlying explanations is causing the varying response when given final size household outbreak data containing mild and severe cases. We conduct numerical studies which show that, given data on sufficiently many households, it is generally possible to discriminate between the two models by comparing the Kullback-Leibler divergence for the two fitted models to these data

Time-dependent CP Asymmetry in B->K* gamma as a (Quasi) Null Test of the Standard Model

We calculate the dominant Standard Model contributions to the time-dependent CP asymmetry in B0->K*0 gamma, which is O(1/mb) in QCD factorisation. We find that, including all relevant hadronic effects, in particular from soft gluons, the asymmetry S is very small, S=-0.022\pm 0.015^{+0}_{-0.01}, and smaller than suggested recently from dimensional arguments in a 1/mb expansion. Our result implies that any significant deviation of the asymmetry from zero, and in particular a confirmation of the current experimental central value, S_{HFAG}=-0.28\pm 0.26, would constitute a clean signal for new physics.Comment: 14 pages, 1 figure, discussions on further power corrections adde