Table 1.

Main Differences between the Deterministic and Stochastic Approach

Character	Deterministic	Stochastic
Model structure	Defined by analytic or ODEs	Defined by a master equation or SDEs
Uncertainty in model dynamics?	No, dynamics is fully determined by parameter values and initial conditions	Yes, the same set of parameter values and initial conditions can lead to different results
Describes	Average behavior of components in a biological system	Stochastic effects that appear in biological systems
Unique outcome?	Yes	No
Variance of process	Variability can be introduced as random effects in model parameters	Is inherent to the system
Population may become extinct in mass action models?	No	Yes
Rate constants	Quantify the rate of specific biological processes/reactions	Might be interpreted as the probability that a biological process/reaction occurs in a very small time interval
Model simulation	ODE solver	•Gillespie or Stochastic Simulation Algorithm: exact method. Requires a probabilistic method involving repeated generation of random numbers •Tau-leaping: approximate and discrete-valued simulation method •SDE solver: continuous approximation
Existing toolkit for parameter estimation and simulation	Large	Small
Computational expense	In general, computationally less demanding than for stochastic models	High
Examples	•Exponential and logistic growth model (see analytic equation from Figure 1 in the main text) •Susceptible–infected–recovered (SIR) model [33]	•Branching process and Moran process (see Box 2 in the main text) •Stochastic SIR models [8,54]