chemical master equation (CME)#

The equation that describes a homogeneously mixed population that can be modeled as a probabilistic combination of states at any given time. Switching between states is determined by a transition rate matrix.

compartmental model#

In epidemiology, a type of mathematical model in which each disease state is treated as a separate compartment and the individuals within each compartment are assumed to be equivalent.

configuration file#

The optional JSON syntax file that specifies the duration of each realization, how many realizations to calculate, and other characteristics of the simulation. If this file is not included, the model runs one realization of Gillespie (SSA) for 100 time units. It often uses a .cfg extension.

cross-entropy method#

A general Monte Carlo approach that is useful for simulations where estimation of very small probabilities is important. It is an iterative method in which a random data sample is generated according to a specified mechanism and then the parameters of the mechanism are updated based on the data to produce a better data sample in the next iteration.


Characterized by the output being fully determined by the parameter values and the initial conditions. Given the same inputs, a deterministic model will always produce the same output.


The file format used to specify the model file that defines the species and mathematics of the model. It stands for Epidemiological Model Language and uses syntax similar to LISP.

event queue#

A data structure that holds events prior to being processed by a receiving program or system.

Gillespie stochastic simulation algorithm (SSA)#

An exact numerical simulation procedure developed by Dan Gillespie in 1977 to describe homogeneous chemical systems. SSA is a type of continuous-time, discrete-state, Markov chain Monte Carlo (MCMC) method.

JSON (JavaScript Object Notation)#

A human-readable, open standard, text-based file format for data interchange. It is typically used to represent simple data structures and associative arrays, and is language-independent. For more information, see

model file#

The required .emodl file that defines the model: the different species, the locale, the mathematics that determine transitions, etc. You will often have one model file and many different configuration files.

Monte Carlo method#

A class of algorithms using repeated random sampling to obtain numerical results. Monte Carlo simulations create probability distributions for possible outcomes, which provides a more realistic way of describing uncertainty.

ordinary differential equation (ODE)#

A differential equation containing one or more functions of one independent variable and its derivatives.

partial differential equation (PDE)#

A differential equation containing unknown multivariable functions and their partial derivatives.

propensity function#

A function that describes the probability of a reaction occurring during the next infinitesimal time interval given the current state.


A single pass of a model through a solver with a given (implicit or explicit) random number stream seed. Most models, due to their stochastic nature, should be run multiple times to generate many realizations in order to characterize the distribution of model states.


A particular algorithm for advancing the state of a model through simulation time. Variations in CMS solvers are similar to the various methods for numerically solving ordinary differential equations.


Borrowed from CME-style models in which a species represents an element or molecule, a species in CMS generally represents a unique state in a disease model, such as susceptible, infectious, or recovered.


Characterized by having a random probability distribution that may be analyzed statistically but not predicted precisely.