This package contains models for estimating epi-curves and individual infection progression distributions simultaneously. The estimators require both total case data by date as well as detailed ("line list") information for a subset of individual.
This models the delay between the onset of symptoms and the presenting/testing/reporting of cases to health authorities. Early in outbreaks these delays can frequently be large due to lack of awareness of the symptoms, however, with increased awareness due to public health information the delays will decrease in time. Even if these delays are constant with time, when estimating their distribution it is necessary to consider both censoring effects and the underlying dynamics of the infection to avoid biases. Conversely, when estimating the dynamics of then infection (e.g. r(t) or R(t)) from reported cases, it is necessary to know these distributions. Therefore, if both infection dynamics and reporting delays are varying at the same time, the best way to account for the biases is to simultaneously estimate both.
The aim of the model is to understand the interaction between the symptom-report time distribution and the underlying dynamics of the infection rate, therefore we use a very simple model for the number of people developing the symptoms each day.
We model the daily growth rate
where
where
where
The symptom-report time distribution must support both positive and negative values. In addition, empirically it is observed that this distribution can be highly skewed with heavy tails, therefore we model it using the Johnson SU distribution which contains 4 parameters
At then end of the reporting period, there may not be many reported case for each symptoms date (since the data is right-censored), therefore there is the option to to make the distribution static after a particular time