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.

Dynamic instabilities in scalar neural field equations with space-dependent delays

In this paper we consider a class of scalar integral equations with a form of space-dependent delay. These non-local models arise naturally when modelling neural tissue with active axons and passive dendrites. Such systems are known to support a dynamic (oscillatory) Turing instability of the homogeneous steady state. In this paper we develop a weakly nonlinear analysis of the travelling and standing waves that form beyond the point of instability. The appropriate amplitude equations are found to be the coupled mean-field Ginzburg-Landau equations describing a Turing-Hopf bifurcation with modulation group velocity of O(1). Importantly we are able to obtain the coefficients of terms in the amplitude equations in terms of integral transforms of the spatio-temporal kernels defining the neural field equation of interest. Indeed our results cover not only models with axonal or dendritic delays but those which are described by a more general distribution of delayed spatio-temporal interactions. We illustrate the predictive power of this form of analysis with comparison against direct numerical simulations, paying particular attention to the competition between standing and travelling waves and the onset of Benjamin-Feir instabilities.

Review of order fulfilment models for Catalogue Mass Customization

Mass Customization (MC) is not a mature business strategy and hence it is not clear that a single or small group of operational models are dominating. Companies tend to approach MC from either a mass production or a customization origin and this in itself gives reason to believe that several operational models will be observable. This paper reviews actual and theoretical fulfilment systems that enterprises could apply when offering a pre-engineered catalogue of customizable products and options. Issues considered are: How product flows are structured in relation to processes, inventories and decoupling point(s); - Characteristics of the OF process that inhibit or facilitate fulfilment; - The logic of how products are allocated to customers; - Customer factors that influence OF process design and operation. Diversity in the order fulfilment structures is expected and is found in the literature. The review has identified four structural forms that have been used in a Catalogue MC context: - fulfilment from stock; - fulfilment from a single fixed decoupling point; - fulfilment from one of several fixed decoupling points; - fulfilment from several locations, with floating decoupling points. From the review it is apparent that producers are being imaginative in coping with the demands of high variety, high volume, customization and short lead times. These demands have encouraged the relationship between product, process and customer to be re-examined. Not only has this strengthened interest in commonality and postponement, but, as is reported in the paper, has led to the re-engineering of the order fulfilment process to create models with multiple fixed decoupling points and the floating decoupling point system