Table 2.
Typical names used to describe the models shown in Figure 1, to assist in literature searches (particularly terms highlighted in italics); descriptions of almost all modelling approaches discussed here are provided in Ref. (21–23), as well as in the references cited throughout this article.
| Figure 1 type | Usual model name/description |
|---|---|
| 1a | Usually referred to as an agent-based model (ABM); sometimes an individual-based model (IBM). Typically, IBMs are less detailed and have fewer state variables than ABMs |
| Reference for bTB (24) | |
| 1b | Usually referred to as a cellular automaton (CA) or probabilistic cellular automaton (PCA) if transitions between time steps are probabilistic |
| 1c | Network model. Note that in the mathematical literature, networks are referred to more precisely as graphs and many results used in epidemiology use graph theory. Approximations to full network models include moment closure methods (including so-called pairwise approximation models or approximations based on triples, etc.) |
| References for foot-and-mouth disease (FMD) (25, 26) | |
| 1d | Agent-based or IBM without spatial information (See 1a), possibly in the form of a branching process model |
| 2a | Sometimes referred to as a metapopulation model or patch model, although there is some confusion in the literature regarding the distinction between these terms. (The confusion focuses on whether to refer to models that maintain individuality but of grouped individuals versus models that consider only whether a patch is occupied or unoccupied, should be referred to as patch models or metapopulations. Both are used.) |
| 2b | Might be referred to as a CA or PCA (see 1b), but where each cell can contain more than one individual. Alternatively, might be referred to a gridded metapopulation model |
| References for bTB (25, 27) | |
| 2c | Network model in which the network connects groups (e.g., herds) rather than individuals |
| Reference for bTB (27) | |
| 2d | Difference equation model or standard Gillespie simulation model (also Gillespie algorithm or Gillespie stochastic simulation algorithm) in which counts of hosts in each state are integer values. Adaptations include tau-leaping approximations |
| 3a | Usually referred to as a metapopulation or patch model. One example in continuous space is the Spatially Realistic Levins Model, in which patches can also have different characteristics |
| Reference for FMD (28) | |
| 3b | CA or PCA (see 1b), where each cell is considered infectious if at least one individual is infectious (see relationship between 1b/2b and 3b) |
| 3c | Network model in which each group is considered infectious if at least one individual is infectious (see relationship between 2c and 3c) |
| For FMD, InterSpread (29, 30) can be used in this way when transmission is not solely a function of distance between farms | |
| 3d | Trivial presence–absence model |
| 4a | Partial differential equation (PDE) model, reaction-diffusion equations |
| 4b | Uncommon in the animal epidemiology literature |
| 4c | Network in which the proportion of animals in each state, per network node, is modelled |
| 4d | Proportion of animals in each state is modelled for a single population. Classic ordinary differential equation (ODE) models fit into this category |
| Reference for FMD (15) |
Not all model types are used in the literature on bTB/FMD, and some, therefore, do not have a reference within this literature. Note that although much of the literature refers to only differential equation models as “compartmental models,” all models referred to in this article are compartmental models in the sense that states are discrete (an individual can only be one state, e.g., susceptible, exposed, infectious, etc.). Depending on the number of states, all could, therefore, be described by reference to the states included, so could be referred to as, e.g., susceptible-infectious-susceptible (SIS), susceptible-infectious-removed, SIR models (those in Figure 1 have only 2 states, so are SI or SIS models).