Individual-based models can encompass a wide range of model forms, and can be designed
to include a variety of complex and detailed host behavior that could not be readily
expressed within the other model types (Nielen et al. 1999; Mangen 2002; Bates et al. 2003;
Noordegraaf et al. 2000; Stacey et al. 2004; see also Section 6.3.5). As the name suggests,
these models consider the dynamics of individuals that occupy a spatial landscape. In
general, these individual-based models have properties in common with both continuousspace
models and stochastic metapopulation models; a transmission kernel is generally
used to capture the spatial spread of infection but this is tempered by the stochastic,
individual-based nature of the population processes leading to a slower rate of spatial
spread (Lewis 2000). Here, as an example of this methodology, we will formulate a general
stochastic individual-based model where each host is capable of localized movement and
transmission is distance dependent; this gives rise to five distinct probabilistic events:
transmission, recovery, birth, death, and movement.
Transmission. Transmission is captured using a technique similar to the integro-differential
equations models. The rate of transmission (or force of infection) to a susceptible
individual, i, is given by: