Glossary of Terms

  • Dimensionality: for a model of the form dy/dt=f(y,t), the dimension of the model is the number of state variables.

  • Initial value (initial condition) : the value of some quantity of interest at some specified time, usually time t=0. For example, if a city had two million inhabitants at the start of year 2000, we might write N(0)=2, where N(t) is the population size, in millions, at time t, measured as years since the start of 2000.

  • Initial value problem: A differential equation, together with an initial condition, such as dy/dt=2-3y, y(0)=2.
    (Remember: a differential equation by itself does not determine a single solution; we also need an initial condition to pick out a specific solution.)

  • Parameter: constants, such as rate constants that appear in a model.

  • State variable: a variable that describes the state of the system. For instance, the population size in a population model, the number of susceptibles or the number of infectives in an epidemic model, or the concentrations of the various chemical species involved in a biochemical reaction network. In simple models, the number of state variables required to specify the state of the system equals the dimensionality of the model.