Quantifying transmission of emerging zoonoses: Using mathematical models to maximize the value of surveillance data

Monique R. Ambrose; Adam J. Kucharski; Pierre Formenty; Jean-Jacques Muyembe-Tamfum; Anne W. Rimoin; James O. Lloyd-Smith

For zero cases to occur in a locality, there must be no zoonotic spillover into that locality 1218 as well as no human-to-human transmission from an outside locality. The zoonotic component is 1219 relatively straightforward to calculate, as it is simply the probability of zero spillover events on 1220 each of the T days (which equals ). The probability of no transmission from an outside 1221 human source is a bit more complicated and can be broken down by the generation of the outside 1222 case to avoid double-counting. The generation of a case indicates how many human-to-human 1223 transmission events occurred leading to the case. We refer to cases resulting from zoonotic 1224 spillover as primary cases. Individuals infected by primary cases are second generation cases, 1225 individuals infected by second generation cases are third generation cases, etc. For there to be no 1226 cases in a locality, no transmission may have occurred into that locality from outside cases in any 1227 generation: 1228 The number of cases caused by a given case (of any generation) in the target locality is 1229 described by a Poisson distribution with expected value equal to Estimating total number of localities under surveillance 1264 We wish to use the estimated parameter values for R, λ z , and σ in conjunction with the 1265 number of observed localities in a broader contact zone (W w ) to estimate the total number of 1266 localities under surveillance in that broader contact zone (V w ). If we let q be the probability a 1267 locality is observed (has one or more cases during the surveillance period), then we expect V w *q 1268 ≈ W w . From the section above, we approximate q = 1-p as: 1269