We investigate the effects of risk perception in a simple model of epidemic spreading. We assume that the perception of the risk of being infected depends on the fraction of neighbors that are ill. The effect of this factor is to decrease the infectivity, that therefore becomes a dynamical component of the model. We study the problem in the mean-field approximation and by numerical simulations for regular, random and scale-free networks. We show that for homogeneous and random networks, there is always a value of perception that stops the epidemics. In the "worst-case" scenario of a scale-free network with diverging input connectivity, a linear perception cannot stop the epidemics; however we show that a non-linear increase of the perception risk may lead to the extinction of the disease. This transition is discontinuous, and is not predicted by the mean-field analysis.

Background: During the HIV infection several quasispecies of the virus arise, which are able to use different coreceptors, in particular the CCR5 and CXCR4 coreceptors (R5 and X4 phenotypes, respectively). The switch in coreceptor usage has been correlated with a faster progression of the disease to the AIDS phase. As several pharmaceutical companies are starting large phase III trials for R5 and X4 drugs, models are needed to predict the co-evolutionary and competitive dynamics of virus strains.

The coexistence of different viral strains (quasispecies) within the same host are nowadays observed for a growing number of viruses, most notably HIV, Marburg and Ebola, but the conditions for the formation and survival of new strains have not yet been understood. We present a model of HIV quasispecies competition, which describes the conditions of viral quasispecies coexistence under different immune system conditions. Our model incorporates both T and B cells responses, and we show that the role of B cells is important and additive to that of T cells. Simulations of coinfection (simultaneous infection) and superinfection (delayed secondary infection) scenarios in the early stages (days) and in the late stages of the infection (years) are in agreement with emerging molecular biology findings. The immune response induces a competition among similar phenotypes, leading to differentiation (quasispeciation), escape dynamics and complex oscillations of viral strain abundance. We found that the quasispecies dynamics after superinfection or coinfection has time scales of several months and becomes even slower when the immune system response is weak. Our model represents a general framework to study the speed and distribution of HIV quasispecies during disease progression, vaccination and therapy. r

Our work stems from the consideration that the spreading of a disease is modulated by the individual's perception of the infected neighborhood and his/her strategy to avoid being infected as well. We introduced a general "cellular agent" model that accounts for a hetereogeneous and variable network of connections. The probability of infection is assumed to depend on the perception that an individual has about the spreading of the disease in her local neighborhood and on broadcasting media. In the one-dimensional homogeneous case the model reduces to the DK one, while for long-range coupling the dynamics exhibits large fluctuations that may lead to the complete extinction of the disease. ⋆