Analytical approximation for invasion and endemic thresholds, and the optimal control of epidemics in spatially explicit individual-based models

Spatial effects in parasite-induced marine diseases of immobile hosts

Emerging marine infectious diseases pose a substantial threat to marine ecosystems and the conservation of their biodiversity. Compartmental models of epidemic transmission in marine sessile organisms, available only recently, are based on non-spatial descriptions in which space is homogenized and parasite mobility is not explicitly accounted for. However, in realistic scenarios epidemic transmission is conditioned by the spatial distribution of hosts and the parasites' mobility patterns, calling for an explicit description of space. In this work, we develop a spatially explicit individual-based model to study disease transmission by waterborne parasites in sessile marine populations. We investigate the impact of spatial disease transmission through extensive numerical simulations and theoretical analysis. Specifically, the effects of parasite mobility into the epidemic threshold and the temporal progression of the epidemic are assessed. We show that larger values of pathogen mobility imply more severe epidemics, as the number of infections increases, and shorter timescales to extinction. An analytical expression for the basic reproduction number of the spatial model, R ~ 0 , is derived as a function of the non-spatial counterpart, R ₀, which characterizes a transition between a disease-free and a propagation phase, in which the disease propagates over a large fraction of the system.