2017-12-12
Different transmission contexts need different responses.
The number of possible transmission trees grows very fast:
for 10 cases with unique onsets, \(\sim 3,500,000\) trees
for 60 cases with unique onsets, \(\sim 8^{81}\) trees (more or less the estimated number of atoms in the universe)
mutations accumulate in the pathogen genome along the transmission chains
can be used to reconstruct transmission trees
For most diseases, whole genome sequences alone are not sufficient for reconstructing transmission trees.
data (e.g. dates of symptom onset) restrict possible trees
combine different types of data to identify a small set of plausible trees
Original outbreaker model used serial interval and genetic data to reconstruct transmission events.
Combines generation time, incubation period, and dates of onset.
Dates of symptom onset (\(t_i\)), generation time (\(w()\)), incubation period (\(f()\)), number of generations (\(\kappa_i\)).
\[ p(t_i | T_i^{inf}) \times p(T_i^{inf} | T_{\alpha_i}^{inf}, \kappa_i) = f(t_i - T_i^{inf}) \times w^{(\kappa_i)}(T_i^{inf} - T_{\alpha_i}^{inf}) \]
Geometric distribution:
\[ p(\kappa_i | \pi) = (1 - \pi^{})^{\kappa_i - 1} \times \pi \]
\[ p(s_i | s_{\alpha_i} \mu) = \mu^{d(s_i, s_{\alpha_i})} \times (1 - \mu)^{(\kappa_i L - d(s_i, s_{\alpha_i}))} \]
Relies on: contact reporting probability (\(\epsilon\)) and probability of contact between non-transmission pairs (\(\lambda\)).
\(\alpha_i = j\): \(p(c_{i,j} = 1 ) = \epsilon\) ; \(p(c_{i,j} = 0) = 1 - \epsilon\)
\(\alpha_i \neq j\): \(p(c_{i,j} = 1) = \lambda \epsilon\) ; \(p(c_{i,j} = 0) = (1 - \lambda) + \lambda (1 - \epsilon)\)