Identification of the relative timing of infectiousness and symptom onset for outbreak control

Robert C. Cope; Joshua V. Ross

Epidemic model 90 We demonstrate using an example system of a novel infectious disease, spreading in a popu-91 lation structured into households. We assume that the population is large and mixing between 92 households is random, such that after a household is initially infected, the remaining transmis-93 sion within the household is independent of transmission outside the household (5, 27). There-94 fore, transmission dynamics within households can be modelled independently (4). Given this 95 novel etiological agent, we wish to determine if symptom onset occurs at the time of infection, 96 infectiousness, or recovery (i.e., these are the three candidate models we wish to discriminate). 97 The model behaviours are otherwise assumed identical. To be emphatic, the underlying disease 98 dynamics is identical in all three models, each differing only in when observations are made, 99 corresponding to different timings of symptom onset (Figure 1a) . 100 101 We model the epidemic dynamics in households as a continuous-time Markov chain ( Figure 102 1a) (15). Individuals transition from susceptible (S) to exposed (E), then to infectious (I), and 103 finally to recovered (R), with rates as described in Table 1. 104 Table 1 : Events, transitions and rates within a household.