Seminário de Biomatemática 21 de Outubro 2008, 16h00 Abstract: Traditional models of infection dynamics assume constant rates for recovery of infected and for loss of immunity of recovered individuals. While this seems a realistic assumption for the process of immunity waning, the infectious period of many infectious diseases is rather well defined, and the recovery profile is closer to deterministic recovery than to exponentially distributed recovery. In a recent paper [1], a generalization of the standard SIRS model that allows for a general recovery profile was proposed and the stability properties of the endemic equilibrium were investigated numerically. This extended model interpolates between exponential and deterministic recovery, which corresponds to the infinite limit of one of the models' parameters, the number of infection stages n. Here we explore this extended SIRS model to investigate the behaviour of long time series of stochastic versions of the SIRS model with deterministic recovery. Stochastic SIRS simulations show that demographic noise amplified by resonance with the system's natural frequency can generate a pattern of recurrent epidemics in long time series [2, 3]. Recently, it was shown that temporal and spatial correlations enhance the amplitude and the coherence of these resonant stochastic fluctuations [4]. In particular, the fluctuation spectrum of long time series of stochastic SIRS simulations with deterministic recovery exhibits significant changes with respect to the power spectrum of the constant recovery rate model, which was computed analytically in [3]. We present an extension of this computation to the general recovery profile model, and an expression in closed form for the theoretical power spectrum for an arbitrary recovery profile with n stages. We give an asymptotic expression for the infinite n limit that corresponds to deterministic recovery. We check the theoretical results against stochastic simulations, and show that we obtain almost perfect agreement. Finally, we discuss how to estimate the recovery profile for different diseases from the incidence data. | back |