Glossary

The terms used across the EpiBranch documentation, with the page that uses each most. Julia syntax is explained in Julia for R users.

Transmission

Secondary cases. The people one case infects. The case that infected them is their infector, and each of them is an infectee.

Potential secondary cases. The people a case would infect if nothing intervened: the number drawn from the offspring distribution. Interventions, a contact's reduced susceptibility or a finite population can prevent some of these infections. The ones prevented stay in the simulation as contacts who were not infected. See Getting started.

Offspring distribution. The distribution of the number of potential secondary cases per case. Without interventions its mean is R.

R (reproduction number). The mean number of secondary cases per case. With no immunity and no control this is R₀. The R in a model is the mean of its offspring distribution; the number realised under interventions is lower.

k (dispersion). How much the number of secondary cases varies between cases. Smaller k means more superspreading: most cases infect nobody and a few infect many. A Poisson offspring distribution is the limit as k becomes large.

NegBin(R, k). The negative binomial offspring distribution with mean R and dispersion k (variance R + R²/k). It returns the Distributions package's NegativeBinomial, whose own parameters are different; build it with NegBin. See Analytical functions.

Multi-type model. A model with several kinds of host (for example age groups), each with its own numbers of secondary cases of each kind. See Multi-type models.

Timing

Times are in whatever unit the delay distributions use; the documentation uses days.

Generation time. The time from the infection of an infector to the infection of an infectee.

Serial interval. The time from symptom onset in an infector to onset in an infectee. EpiBranch models generation times; serial intervals follow from them and the incubation period.

Incubation period. The time from infection to symptom onset, given with clinical_presentation. See Getting started.

Contact interval. In network and household models, the time from the start of an infector's infectious period (by default their infection) to a contact with a particular person that would infect them if nothing intervened. See Covariates and time-varying transmission.

Index case. A case an outbreak starts from. simulate starts from one unless you set n_initial.

Control

Isolation. Removing a known case from transmission, usually some time after symptom onset. See Isolation and contact tracing.

Quarantine. Removing a traced contact, who is not (yet) a known case, from transmission from the time they are traced. Quarantine reaches contacts before they develop symptoms, including those who were never infected.

Isolation and quarantine duration. How long isolation or quarantine lasts, set with duration on Isolation and Quarantine: a number of days, a distribution, or a function of the random number generator and the individual, (rng, ind) -> .... When it ends the person is released, and one who is still infectious can transmit again. duration = Inf means they are never released. When a duration is finite, the line list records the release date in date_isolation_release.

Interventions. The control measures in a model: isolation, contact tracing, ring and mass vaccination, post-exposure prophylaxis, and others. Each potential infection goes ahead only if no measure prevents it first; survival analysis calls this competing risks. See Isolation and contact tracing and Vaccination.

Containment probability. The proportion of simulated outbreaks in which transmission stopped before reaching the case cap (max_cases), the generation cap or the time cap. containment_probability calculates it from simulations and includes every intervention in the model. probability_contain gives a closed-form version for simpler control.

Extinction probability. The probability that transmission from one index case dies out, calculated exactly from the offspring distribution by extinction_probability. It ignores the population characteristics in a model. Any intervention with no closed-form effect on the offspring distribution stops it with an error, which today means every intervention in the package. To see what control adds, run it on the process without interventions and compare the answer with the containment probability from simulations. Its complement is epidemic_probability. See Analytical functions.

Models and outputs

Model. In these pages, the transmission process together with everything added to it: population characteristics, interventions, clinical progression and how cases are observed. In code a model is a transmission process (such as BranchingProcess) on its own, or wrapped in a ModelSpec that adds the other parts. See Getting started.

Scenario. One set of parameters and interventions to compare with others, for example the same pathogen with and without contact tracing.

Population characteristics (attributes). Characteristics each person is given when they enter the simulation, such as age, incubation period or whether they will develop symptoms. They are passed to a model as attributes, built with functions such as clinical_presentation and demographics. See Line lists and contacts.

Clinical progression. The sequence of clinical events a case goes through, such as onset, reporting, admission and recovery or death. See Clinical transitions.

Line list. A table with one row per case and columns such as infection date, onset date, isolation and tracing status, as from outbreak surveillance. linelist builds one from a simulation; contacts builds the matching table with one row per contact. See Line lists and contacts.

Transmission chain. All the cases descending from one index case. Chain size is the number of cases in it, including the index case; chain length is the number of generations after the index case. See Chain statistics.

Borel and gamma-Borel distributions. The distribution of chain sizes when the offspring distribution is Poisson (Borel), and when R also varies between chains following a gamma distribution (gamma-Borel). See Chain statistics.

Inference

Confidence interval. An interval from maximum-likelihood estimation, such as a profile-likelihood interval. See Inference.

Credible interval. An interval from the quantiles of a Bayesian posterior distribution. See Inference.