Alberto A. Pinto

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For the spatial stochastic epidemic reinfection model SIRI, where susceptibles S can become infected I, then recover and remain only partial immune against reinfection R, we determine the phase transition lines using pair approximation for the moments derived from the master equation. We introduce a scaling argument that allows us to determine analytically(More)
Sullivan's scaling function provides a complete description of the smooth conjugacy classes of cookie-cutters. However, for smooth conjugacy classes of Markov maps on a train track, such as expanding circle maps and train track mappings induced by pseudo-Anosov systems, the generalisation of the scaling function suuers from a deeciency. It is diicult to(More)
Recently, the notion of a reinfection threshold in epidemiological models of only partial immunity has been debated in the literature. We present a rigorous analysis of a model of reinfection which shows a clear threshold behaviour at the parameter point where the reinfection threshold was originally described. Furthermore, we demonstrate that this(More)
In the paper we discuss two questions about smooth expanding dynam-ical systems on the circle. (i) We characterize the sequences of asymptotic length ratios which occur for systems with Hölder continuous derivative. The sequence of asymptotic length ratios are precisely those given by a positive Hölder continuous function s (solenoid function) on the Cantor(More)
2007/Jul/02 Sensibility of quorum growth thresholds controlling local immune responses – p. 2007/Jul/02 Sensibility of quorum growth thresholds controlling local immune responses – p. 2/36 Motivation 2007/Jul/02 Sensibility of quorum growth thresholds controlling local immune responses – p. 3/36 Immune system Leukocytes (white blood cells) circulate in the(More)