Glossary

addition-deletion process
A process that adds and removes nodes from a network. The usual model (due to Moore et alia) adds nodes at a constant rate and with constant degree, removes nodes randomly at a constant rate, and connects new nodes to existing nodes according to some probabilistic attachment kernel.
compartments
The possible dynamical states in a compartmented model of disease.
compartmented model of disease
A disease model that represents the progression of a disease as a set of discrete compartments with transitions possible between them. Transitions typically occur with some base probability, which might be fixed or might vary across the course of the simulation. See Hethcote for a survey,
contact tree

The way in which individuals were infected during thhe infection. Each node is an infected individual, with edges representing the individuals that individual infected.

While it’s common talk of a contact tree, this will only be the case if there is an identifiable “patient zero” from whom all infections arise. In the more general case of multiple people initially infected, the contact tree will actually be a contact forest of multiple independent trees, each one rooted at an initially-infected individual.

continuous time
A simulation mode in which events occur at unique times represented by real numbers. No two events ever happen simultaneously, but they can be separated by an arbitrarily small interval. Continuous-time simulations can be made statistically exact and run faster for situations in which there are long periods where no events occur.
discrete time
A simulation mode in which time progresses in single integer timesteps. During each timestep a collection of events can occur. Discrete-time simulations can be easier to code and understand.
dynamical state
The state of a node or edge at some point in the simulation. These typically reflect the compartments of the simulation, but may be more complex and comprise a vector of information.
event
A simulation event that changes the state of the underlying network or simulation. Events can occur in continuous time or discrete time.
event function
A function called when an event fires to perform the action required. Event functions take three arguments: the current simulation time and the element at which the event occurs (which will be selected by the chosen process dynamics). Elements are typically either nodes or edges, depending in the locus at which the event occurs.
Gillespie simulation
A simulation technique developed initially for ab initio chemistry simulations. See Gillespie 1976 and Gillespie 1977.
locus
A “place” at which dynamics can occur, that is to say, where nodes can change compartments and any other tasks can happen. Each event is associated with a particular locus: the locus contains the set of nodes or edges to which the event may be applied, while the event defines what happens. ALl loci are derived from the Locus class.
network generator
A process that samples a class of random networks to create an instance. A typical example is the class of networks with Poisson degree distribution (the ER networks), defined by the order and mean degree of the network.
posted event
An event posted for a definite future time. The process dynamics will execute the posted events at the appropriate time
process dynamics
The simulation approach used, which selects how and when each event fires. Process dynamics execute events in time order from two possible sources: a random distribution that chooses an event based on their relative probability or rate; and any posted event that has been scheduled.
SIS
A compartmented model of disease where nodes go from being Susceptible to the disease, to Infected and able to infect others, and then recover back to Susceptible.
SIR
A compartmented model of disease where nodes go from being Susceptible to the disease, to Infected and able to infect others, and are then Removed and take no further part in the dynamics.
stochastic process
A process whose exact progression is determined by random variables drawn from particular probability distributions.
stochastic dynamics
Also known as Gillespie dynamics, this process dynamics operates in continuous time with one event occurring at each time point.
synchronous dynamics
A process dynamics using discrete time, where a simulation passes through a sequence of discrete timesteps which may include several (or no) events happening.