Article

# Meta-analysis of the risks of hypertension and QTc prolongation in patients with advanced non-small cell lung cancer who were receiving vandetanib

University of Lisbon, Lisboa, Lisbon, Portugal
(Impact Factor: 2.29). 05/2009; 79(4 Pt 1):041922. DOI: 10.1103/PhysRevE.79.041922
Source: PubMed

ABSTRACT

We show that the simplest stochastic epidemiological models with spatial correlations exhibit two types of oscillatory behavior in the endemic phase. In a large parameter range, the oscillations are due to resonant amplification of stochastic fluctuations, a general mechanism first reported for predator-prey dynamics. In a narrow range of parameters that includes many infectious diseases which confer long lasting immunity the oscillations persist for infinite populations. This effect is apparent in simulations of the stochastic process in systems of variable size and can be understood from the phase diagram of the deterministic pair approximation equations. The two mechanisms combined play a central role in explaining the ubiquity of oscillatory behavior in real data and in simulation results of epidemic and other related models.

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• "In discrete-time models, global oscillations have been reported [19– 22] and understood analytically [23]. In continuous-time models, the situation is different: in the standard SIRS model with diffusive coupling [24], global oscillations seem not to be stable, even in the favorable condition of global or random coupling [24] [25] [26] [27]. "
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Physical Review E 11/2009; 80(5 Pt 1):051915. DOI:10.1103/PhysRevE.80.051915 · 2.29 Impact Factor
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##### Article: Discontinuous nonequilibrium phase transitions in a nonlinearly pulse-coupled excitable lattice model
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ABSTRACT: We study a modified version of the stochastic susceptible-infected-refractory-susceptible (SIRS) model by employing a nonlinear (exponential) reinforcement in the contagion rate and no diffusion. We run simulations for complete and random graphs as well as d-dimensional hypercubic lattices (for d=3,2,1). For weak nonlinearity, a continuous nonequilibrium phase transition between an absorbing and an active phase is obtained, such as in the usual stochastic SIRS model [Joo and Lebowitz, Phys. Rev. E 70, 036114 (2004)]. However, for strong nonlinearity, the nonequilibrium transition between the two phases can be discontinuous for d>or=2, which is confirmed by well-characterized hysteresis cycles and bistability. Analytical mean-field results correctly predict the overall structure of the phase diagram. Furthermore, contrary to what was observed in a model of phase-coupled stochastic oscillators with a similar nonlinearity in the coupling [Wood, Phys. Rev. Lett. 96, 145701 (2006)], we did not find a transition to a stable (partially) synchronized state in our nonlinearly pulse-coupled excitable elements. For long enough refractory times and high enough nonlinearity, however, the system can exhibit collective excitability and unstable stochastic oscillations.
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