Journal ArticleDOI
An age-structured model of pre- and post-vaccination measles transmission.
TLDR
An age-structured epidemiologic model is investigated here, which also pays attention to the fact that children are promoted grade-wise into and out of school, and is shown to perform better than previous global mass-action models.Abstract:
An infection like measles does not spread uniformly in populations from Europe and North America. Of special importance is a pronounced age-dependency in the contact rates, because of increased infection transmission within schools. Therefore an age-structured epidemiologic model is investigated here, which also pays attention to the fact that children are promoted grade-wise into and out of school. Simulation results are contrasted with pre- and post-vaccination measles data from England and Wales and the model is shown to perform better than previous global mass-action models.read more
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Journal ArticleDOI
The Mathematics of Infectious Diseases
TL;DR: Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.
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Travelling waves and spatial hierarchies in measles epidemics
TL;DR: This work demonstrates recurrent epidemic travelling waves in an exhaustive spatio-temporal data set for measles in England and Wales and uses wavelet phase analysis, which allows for dynamical non-stationarity—a complication in interpreting spatio–temporal patterns in these and many other ecological time series.
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Herd Immunity: History, Theory, Practice
TL;DR: This new popularity of herd immunity comes as a consequence of several recent major achievements of vaccination programs, i.e.: the historic success of the global smallpox eradication program; dramatic increases in vaccination coverage stimulated by national programs and by the Expanded Programme on Immunization.
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Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models
TL;DR: When the traditional assumption that the incidence rate is proportional to the product of the numbers of infectives and susceptibles is dropped, the SIRS model can exhibit qualitatively different dynamical behaviors, including Hopf bifurcations, saddle-node bifuriations, and homoclinic loop bifURcations.
Journal ArticleDOI
Using Data on Social Contacts to Estimate Age-specific Transmission Parameters for Respiratory-spread Infectious Agents
TL;DR: In this article, the authors estimated age-specific transmission parameters by augmenting infectious disease data with auxiliary data on self-reported numbers of conversational partners per person, and they showed that models that use transmission parameters based on these selfreported social contacts are better able to capture the observed patterns of infection of endemically circulating mumps, as well as observed pattern of spread of pandemic influenza.