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Abstract: This paper is concerned with SIR susceptible $\to$ infected $\to$ removedhousehold epidemic models in which the infection response may be either mild orsevere, with the type of response also affecting the infectiousness of anindividual. Two different models are analysed. In the first model, theinfection status of an individual is predetermined, perhaps due to partialimmunity, and in the second, the infection status of an individual depends onthe infection status of its infector and on whether the individual was infectedby a within- or between-household contact. The first scenario may be modelledusing a multitype household epidemic model, and the second scenario by a modelwe denote by the infector-dependent-severity household epidemic model. Largepopulation results of the two models are derived, with the focus being on thedistribution of the total numbers of mild and severe cases in a typicalhousehold, of any given size, in the event that the epidemic becomesestablished. The aim of the paper is to investigate whether it is possible todetermine which of the two underlying explanations is causing the varyingresponse when given final size household outbreak data containing mild andsevere cases. We conduct numerical studies which show that, given data onsufficiently many households, it is generally possible to discriminate betweenthe two models by comparing the Kullback-Leibler divergence for the two fittedmodels to these data.

Author: Frank Ball, Tom Britton, David Sirl


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