Spatiotemporal sine-Wiener Bounded Noise and its effect on Ginzburg-Landau model

In this work, we introduce a kind of spatiotemporal bounded noise derived by the sine-Wiener noise and by the spatially colored unbounded noise introduced by Garc\'ia-Ojalvo, Sancho and Ram\'irez-Piscina (GSR noise). We characterize the behavior of the distribution of this novel noise by showing its dependence on both the temporal and the spatial autocorrelation strengths. In particular, we show that the distribution experiences a stochastic transition from bimodality to trimodality. Then, we employ the noise here defined to study phase transitions on Ginzburg-Landau model. Various phenomena are evidenced by means of numerical simulations, among which re-entrant transitions, as well as differences in the response of the system to GSR noise additive perturbations. Finally, we compare the statistical behaviors induced by the sine-Wiener noise with those caused by 'equivalent' GSR noises.Comment: 17 pages, 13 figure

Lyapunov Stability of an SIRS epidemic model with varying population: ecological VS physical approaches

We consider a general SIRS epidemiological transmission model for an endemic infection with variable population including a general assumption of density-dependent mortality and vertical transmission. We analyse global stability by the Lyapunov approach, proposing two alternative Lyapunov functions. The first one is based on traditional ecological arguments, while the second one is a 'physical' Lyapunov function based on the energy of an appropriate second order equation. Both functions allow to prove the global stability of the (unique) endemic state under broad - not equivalent - parametric conditions. This suggests that using different Lyapunov functions provide useful complementary information on the parametric regions where global stability prevails

Lyapunov stability of an SIRS epidemic model with varying population

In this paper we consider an SIRS epidemic model under a general assumption of density-dependent mortality. We prove the global stability of the disease-free equilibrium and propose a Lyapunov function that allows to demonstrate the global stability of the (unique) endemic state under broad conditions.Comment: 7 page

Fine-tuning anti-tumor immunotherapies via stochastic simulations

Background: Anti-tumor therapies aim at reducing to zero the number of tumor cells in a host within their end or, at least, aim at leaving the patient with a sufficiently small number of tumor cells so that the residual tumor can be eradicated by the immune system. Besides severe side-effects, a key problem of such therapies is finding a suitable scheduling of their administration to the patients. In this paper we study the effect of varying therapy-related parameters on the final outcome of the interplay between a tumor and the immune system.Results: This work generalizes our previous study on hybrid models of such an interplay where interleukins are modeled as a continuous variable, and the tumor and the immune system as a discrete-state continuous-time stochastic process. The hybrid model we use is obtained by modifying the corresponding deterministic model, originally proposed by Kirschner and Panetta. We consider Adoptive Cellular Immunotherapies and Interleukin-based therapies, as well as their combination. By asymptotic and transitory analyses of the corresponding deterministic model we find conditions guaranteeing tumor eradication, and we tune the parameters of the hybrid model accordingly. We then perform stochastic simulations of the hybrid model under various therapeutic settings: constant, piece-wise constant or impulsive infusion and daily or weekly delivery schedules.Conclusions: Results suggest that, in some cases, the delivery schedule may deeply impact on the therapy-induced tumor eradication time. Indeed, our model suggests that Interleukin-based therapies may not be effective for every patient, and that the piece-wise constant is the most effective delivery to stimulate the immune-response. For Adoptive Cellular Immunotherapies a metronomic delivery seems more effective, as it happens for other anti-angiogenesis therapies and chemotherapies, and the impulsive delivery seems more effective than the piece-wise constant. The expected synergistic effects have been observed when the therapies are combined. \ua9 2012 Caravagna et al.; licensee BioMed Central Ltd