When a disease breaks out in a human population, changes in behavior in response to the outbreak can alter the progression of the infectious agent. In particular, people aware of a disease in their proximity can take measures to reduce their susceptibility. Even if no centralized information is provided about the presence of a disease, such awareness can arise through first-hand observation and word of mouth. To understand the effects this can have on the spread of a disease, we formulate and analyze a mathematical model for the spread of awareness in a host population, and then link this to an epidemiological model by having more informed hosts reduce their susceptibility. We find that, in a well-mixed population, this can result in a lower size of the outbreak, but does not affect the epidemic threshold. If, however, the behavioral response is treated as a local effect arising in the proximity of an outbreak, it can completely stop a disease from spreading, although only if the infection rate is below a threshold. We show that the impact of locally spreading awareness is amplified if the social network of potential infection events and the network over which individuals communicate overlap, especially so if the networks have a high level of clustering. These findings suggest that care needs to be taken both in the interpretation of disease parameters, as well as in the prediction of the fate of future outbreaks. mathematical model | rumor spread | behavioral response | social networks H uman reactions to the presence of disease abound, yet they have rarely been systematically investigated (1). Such reactions can range from avoiding social contact with infected individuals (social distancing) to wearing protective masks, vaccination, or more creative precautions. It has been shown, for instance, that local measles outbreaks are correlated with the demand for measles, mumps, and rubella vaccines (2). Similarly, the demand for condoms rises in areas where AIDS is prevalent (3), and condom use has been linked to the knowledge of someone who has died of AIDS (4).Behavior that is responsive to the presence of a disease can potentially reduce the size of an epidemic outbreak. On closer inspection, it is not so much the presence of the disease itself that will prompt humans to change their behavior, as awareness of the presence of the disease. A change in behavior can be prompted without witnessing the disease first hand, but by being informed about it through others. This information in itself will spread through the population and have its own dynamic. For example, according to the Chinese Southern Weekend newspaper, the text message "There is a fatal flu in Guangzhou" was sent 126 million times in Guangzhou alone during the 2003 severe acute respiratory syndrome (SARS) outbreak (5), causing people to stay home or wear face masks when going outside. This figure stands in stark contrast to the comparatively low number of 5,327 cases recorded in the whole of China (6). It is not clear how much the individual behaviora...

Habitat and species richness in drylands are affected by the dynamics of a few key species, termed "ecosystem engineers." These species modulate the landscape and redistribute the water resources so as to allow the introduction of other species. A mathematical model is developed for a pair of ecosystem engineers commonly found in drylands: plants forming vegetation patterns and cyanobacteria forming soil crusts. The model highlights conditions for habitat creation and for high habitat richness, and suggests a novel mechanism for species loss events as a result of environmental changes.

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The spread of a contagious disease is often accompanied by a rise in awareness of those in the social vicinity of infected individuals, and a subsequent change in behaviour. Such reactions can manifest themselves in lower susceptibility as people try to prevent themselves from catching the disease, but also in lower infectivity because of self-imposed quarantine or better hygiene, shorter durations of infectiousness or longer immunity. We here focus on the scenario of an endemic disease of which members of the population can be either aware or unaware, and consider a broad set of possible reactions. We quantify the impact on the endemicity of a disease in a well-mixed population under the variation of different disease parameters as a consequence of growing awareness in the population. Applying a pair-closure scheme allows us to analyse the effect of local correlations if aware individuals tend to occur near infected cases, and to link this to the amount of overlap between the networks underlying the spread of awareness and disease, respectively. Lastly, we study the consequences on the dynamics when the pathogen and awareness spread at different velocities.

by recovery as an hysteresis loop and sheds light on the irreversibility of desertification.

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Vegetation patches in drylands are localized structures of biomass and water. We study these structures using a mathematical modeling approach that captures biomass-water feedbacks. Biomass-water structures are found to differ in their spatial forms and ecological functions, depending on species type, soil conditions, precipitation range, and other environmental factors. Asymptotic spot structures can destabilize to form ring structures, expanding in the radial direction, or crescent structures, migrating uphill. Stable spot structures can differ in their soil-water distributions, forming water-enriched patches or water-deprived patches. The various biomass-water structures are expected to function differently in the context of a plant community, forming landscapes of varying species diversity.