Pathogen genetic variation in small-world host contact structures

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Abstract
We introduce a model for assessing the levels and patterns of genetic diversity in pathogen populations, whose epidemiology follows a susceptible- infected-susceptible model. We assume a population which is structured into many small subpopulations (hosts) that exchange migrants (transmission) between their neighbours. We consider that the hosts are connected according to a small-world network topology, and in this way our model interpolates between two classical population genetics models: the stepping-stone and the island model. We have observed that the level of diversity has a maximum at intermediate values of the basic reproductive number R0. This result is independent of the topology considered, but depends on the relation between parasite load and the rate at which the immune system clears the pathogen. We show that, for a given R0 of the pathogen, as the host contact structure changes, by increasing the rewiring probability p, the level of pathogen diversity decreases. Its level is higher in regular lattices and smaller in random graphs. The latter topology presents a similar diversity level to the island model (a fully connected network), but also presents a clear pattern of isolation by distance, which is observed in some pathogen populations.