The spontaneous behavioral responses of individuals to the progress of an epidemic are recognized to have a significant impact on how the infection spreads. One observation is that, even if the infection strength is larger than the classical epidemic threshold, the initially growing infection can diminish as the result of preventive behavioral patterns adopted by the individuals. In order to investigate such dynamics of the epidemic spreading, we use a simple behavioral model coupled with the individual-based SIS epidemic model where susceptible individuals adopt a preventive behavior when sensing infection. We show that, given any infection strength and contact topology, there exists a region in the behavior-related parameter space such that infection cannot survive in long run and is completely contained. Several simulation results, including a spreading scenario in a realistic contact network from a rural district in the State of Kansas, are presented to support our analytical arguments.

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The fluorescence of the single tryptophan in Bacillus stearothermophilus phosphofructokinase was characterized by steady-state and time-resolved techniques. The enzyme is a tetramer of identical subunits, which undergo a concerted allosteric transition. Time-resolved emission spectral data were fitted to discrete and distributed lifetime models. The fluorescence decay is a double exponential with lifetimes of 1.6 and 4.4 ns and relative amplitudes of 40 and 60%. The emission spectra of both components are identical with maxima at 327 nm. The quantum yield is 0.31 +/- 0.01. The shorter lifetime is independent of temperature; the longer lifetime has weak temperature dependence with activation energy of 1 kcal/mol. The fluorescence intensity and decay are the same in H2O and D2O solutions, indicating that the indole ring is not accessible to bulk aqueous solution. The fluorescence is not quenched significantly by iodide, but it is quenched by acrylamide with bimolecular rate constant of 5 x 10(8) M-1 s-1. Static and dynamic light scattering measurements show that the enzyme is a tetramer in solution with hydrodynamic radius of 40 A. Steady-state and time-resolved fluorescence anisotropies indicate that the tryptophan is immobile. The allosteric transition has little effect on the fluorescence properties. The fluorescence results are related to the x-ray structure.

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