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Epidemic spread in single-host systems strongly depends on the population's transmission network. However, little is known regarding the spread of epidemics across networks representing populations of multiple hosts. We explored cross-species transmission in a multilayer network where layers represent populations of two distinct hosts, and disease can spread across intralayer (within-host) and interlayer (between-host) edges. We developed an analytic framework for the SIR epidemic model to examine the effect of (i) source of infection and (ii) between-host asymmetry in infection probabilities, on disease risk. We measured risk as outbreak probability and outbreak size in a focal host, represented by one network layer. Numeric simulations were used to validate the analytic formulations. We found that outbreak probability is determined by a complex interaction between source of infection and between-host infection probabilities, whereas outbreak size is mainly affected by the non-focal host to focal host infection probability. Hence, inter-specific asymmetry in infection probabilities shapes disease dynamics in multihost networks. These results highlight the importance of considering multiple measures of disease risk and advance our understanding of disease spread in multihost systems. The study provides a flexible way to model disease dynamics in multiple hosts while considering contact heterogeneity within and between species. We strongly encourage empirical studies that include information on both cross-species infection rates and network structure of multiple hosts. Such studies are necessary to corroborate our theoretical results and to improve our understanding of multihost epidemiology., (Copyright © 2017 Elsevier Ltd. All rights reserved.)

Understanding how desertification takes place in different ecosystems is an important step in attempting to forecast and prevent such transitions. Dryland ecosystems often exhibit patchy vegetation, which has been shown to be an important factor on the possible regime shifts that occur in arid regions in several model studies. In particular, both gradual shifts that occur by front propagation, and abrupt shifts where patches of vegetation vanish at once, are a possibility in dryland ecosystems due to their emergent spatial heterogeneity. However, recent theoretical work has suggested that the final step of desertification - the transition from spotted vegetation to bare soil - occurs only as an abrupt shift, but the generality of this result, and its underlying origin, remain unclear. We investigate two models that detail the dynamics of dryland vegetation using a markedly different functional structure, and find that in both models the final step of desertification can only be abrupt. Using a careful numerical analysis, we show that this behavior is associated with the disappearance of confined spot-pattern domains as stationary states, and identify the mathematical origin of this behavior. Our findings show that a gradual desertification to bare soil due to a front propagation process can not occur in these and similar models, and opens the question of whether these dynamics can take place in nature., (Copyright © 2017 Elsevier Ltd. All rights reserved.)