Modelling pathogen transmission: the interrelationship between local and global approaches

We describe two spatial (cellular automaton) host-pathogen models with contrasting types of transmission, where the biologically realistic transmission mechanisms are based entirely on 'local' interactions. The two models, fixed contact area (FCA) and fixed contact number (FCN), may be viewed as local 'equivalents' of commonly used global density- (and frequency-) dependent models. Their outputs are compared with each other and with the patterns generated by these global terms. In the FCN model, unoccupied cells are bypassed, but in the FCA model these impede pathogen spread, extending the period of the epidemic and reducing the prevalence of infection when the pathogen persists. Crucially, generalized linear modelling reveals that the global transmission terms betaSI and beta'SI/N are equally good at describing transmission in both the FCA and FCN models when infected individuals are homogeneously distributed and N is approximately constant, as at the quasi-equilibrium. However, when N varies, the global frequency-dependent term beta'SI/N is better than the density-dependent one, betaSI, at describing transmission in both the FCA and FCN models. Our approach may be used more generally to compare different local contact structures and select the most appropriate global transmission term.