Table 1 Overview of dynamic modeling methods

Discrete dynamic models

Discrete time and discrete (abstract) state

Modeling of Bordetella infection pathogenesis, T cell receptor signaling

Can deal with many components but the simple state description cannot replicate continuous variation of immune components.

[6, 44–47]

Continuous-discrete hybrid models (e.g. piecewise linear differential equations)

Combination of discrete and continuous state, continuous time

Modeling of infection pathogenesis and pathogen time-courses

The number of components that can be modeled is smaller than in discrete models because of the increase in the number of parameters. The state of the variables may not be directly comparable with experimental measurements. Although there are few parameters per component, parameter estimation becomes an issue for large systems.

[7, 36]

Differential equations

Continuous time and state

SIR (Susceptible Infectious and Recovered) models of target cells and pathogens, T cell differentiation

The variables of the model can reproduce the experimentally observed concentrations. Insufficient data to inform the functional forms and parameter values can limit the use of this method. Less scalable than discrete approaches.

[11, 13, 20]

Finite state automata (e.g. agent-based models)

Discrete states (abstraction of cell state), discrete space and continuous time

Cell to cell communications

Simplified way to simulate spatial aspects. Can handle a few immune components in detail. Computationally expensive.

[48–50]

Partial differential equations

Continuous time, state and space

Transport of cells across vascular membranes

Appropriate to model a few immune components in detail. Computationally expensive and the determination of parameters is rather difficult.

[51, 52]