deletions | additions       diff --git a/subsubsection_Results_from_national_TB__.tex b/subsubsection_Results_from_national_TB__.tex  index 8fabf3c..d816953 100644  --- a/subsubsection_Results_from_national_TB__.tex  +++ b/subsubsection_Results_from_national_TB__.tex 
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$i(N - C)\Delta t - m C\Delta t = 0$  $i = \frac{C}{N \frac{C}{d(N  - C} d^{-1} C)}  = \frac{P}{1 \frac{P}{d(1  - P} d^{-1}$ P)}$  In practice, the duration of disease cannot be directly measured. For example, measurements of the duration of symptoms in prevalent TB cases that are detected during a prevalence survey are systematically biased towards lower values, since active case-finding truncates the natural history of undiagnosed disease. Measurements of the duration of disease in notified cases ignore the duration of disease among non-notified and untreated cases.