Emergent trade-offs and selection for outbreak frequency in spatial epidemics

Abstract

Nonspatial theory on pathogen evolution generally predicts selection for maximal number of secondary infections, constrained only by supposed physiological trade-offs between pathogen infectiousness and virulence. Spread of diseases in human populations can, however, exhibit large scale patterns, underlining the need for spatially explicit approaches to pathogen evolution. Here, we show, in a spatial model where all pathogen traits are allowed to evolve independently, that evolutionary trajectories follow a single relationship between transmission and clearance. This tradeoff relation is an emergent system property, as opposed to being a property of pathogen physiology, and maximizes outbreak frequency instead of the number of secondary infections. We conclude that spatial pattern formation in contact networks can act to link infectiousness and clearance during pathogen evolution in the absence of any physiological trade-off. Selection for outbreak frequency offers an explanation for the evolution of pathogens that cause mild but frequent infections.evolution ͉ pathogen ͉ spatial model ͉ spatial patterns C urrent theory on pathogen evolution places much emphasis on physiological (or life-history) trade-offs that relate virulence, infectiousness, mode of transmission, and immune clearance (1-6). These trade-offs, motivated by a supposed functional link between two (or more) traits, specify that evolutionary improvements in one trait are necessarily accompanied by a decline in another (7,8). One of the most commonly made trade-off assumptions is that increased production of transmission stages causes increased host mortality and thereby shortens the infection period (9). Where traits can evolve independently, nonspatial theory typically predicts selection for maximal transmissibility and infection period, thus maximizing the number of secondary infections (i.e., the number of new infections an infected host causes). It is commonly held, however, that the benefits of increased transmission and the associated penalties of virulence and shorter infection are balanced so that the number of secondary infections is maximized at intermediate transmissibility and virulence (2). In simple nonspatial models, this evolutionary maximization corresponds to selection for maximal basic reproductive ratio R 0 (10), i.e., the expected number of secondary infections in an unexposed population [but note that this result depends on absence of multiple infections (5) and vertical transmission (11, 12)]. The current popularity of tradeoffs in studies of pathogen evolution stems from the fact that they provide a possible explanation for selection for intermediate virulence and transmissibility (8), and that they can be used to predict pathogen evolution in response to human interventions such as the use of imperfect vaccines (4) or improved hygiene (13). However, the exact shape (and even existence) of trade-offs is unknown for many diseases (14).A growing body of work reports on the role of spatial pattern formation on evolutionary pro...

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Spatial organization and evolution period of the epidemic model using cellular automata

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