Author
Giuseppe Mulone
Other affiliations: Durham University
Bio: Giuseppe Mulone is an academic researcher from University of Catania. The author has contributed to research in topics: Nonlinear system & Reynolds number. The author has an hindex of 21, co-authored 63 publications receiving 1269 citations. Previous affiliations of Giuseppe Mulone include Durham University.
Papers published on a yearly basis
Papers
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TL;DR: In this paper, an epidemic model is proposed to describe the dynamics of disease spread between two patches due to population dispersal, and it is proved that reproduction number is a threshold of the uniform persistence and disappearance of the disease.
118 citations
TL;DR: In this article, a predator-prey model with a stage structure for the predator is proposed, which improves the assumption that each individual predator has the same ability to capture prey.
116 citations
TL;DR: It is shown that the steady states of the White and Comiskey model of heroin epidemics are stable and this model is applicable to heroin treatment and ODE modelling.
Abstract: We show that the steady states of the White and Comiskey [E. White, C. Comiskey, Heroin epidemics, treatment and ODE modelling, Math. Biosci. 208 (2007) 312–324.] model of heroin epidemics are stable.
101 citations
TL;DR: In this article, the Lyapunov direct method was used to obtain necessary and sufficient conditions of conditional nonlinear stability for the magnetic Benard problem with a suitable change of fields and a generalized energy functional.
Abstract: We study the magnetic Benard problem with the Lyapunov direct method and obtain necessary and sufficient conditions of conditional nonlinear stability. By introducing a suitable change of fields and a generalized energy functional, we show that, whenever the magnetic Prandtl number is less than the usual Prandtl number, the critical linear and nonlinear stability Rayleigh numbers coincide for any Chandrasekhar number.
88 citations
TL;DR: In this paper, the nonlinear stability of the motionless state of a binary fluid mixture heated and salted from below, in the Oberbeck-Boussinesq scheme, was studied in the stress-free boundary case.
Abstract: The nonlinear stability of the motionless state of a binary fluid mixture heated and salted from below, in the Oberbeck-Boussinesq scheme, is studied, in the stress-free boundary case. A stabilizing effect of gradient of solute on thermal convection is shown and a globally nonlinear exponential stability theorem is proved. In particular, when the ratio r of the Schmidt and the Prandtl number is less than 1, a region of coincidence of linear and nonlinear critical parameters is found. The stability of plane parallel convective flows (plane Couette and Poiseuille flows with linear temperature and concentration profiles) is also studied. Stability conditions independent of Reynolds number are found.
59 citations
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Journal Article•
28,685 citations
2,084 citations
Book•
01 Jan 1991TL;DR: In this paper, the Third Edition of the Third edition of Linear Systems: Local Theory and Nonlinear Systems: Global Theory (LTLT) is presented, along with an extended version of the second edition.
Abstract: Series Preface * Preface to the Third Edition * 1 Linear Systems * 2 Nonlinear Systems: Local Theory * 3 Nonlinear Systems: Global Theory * 4 Nonlinear Systems: Bifurcation Theory * References * Index
1,977 citations
TL;DR: In this article, the basic reproduction ratio and its computation formulae are established for a large class of compartmental epidemic models in periodic environments, and it is proved that a disease cannot invade the disease-free state if the ratio is less than unity and can invade if it is greater than unity.
Abstract: The basic reproduction ratio and its computation formulae are established for a large class of compartmental epidemic models in periodic environments. It is proved that a disease cannot invade the disease-free state if the ratio is less than unity and can invade if it is greater than unity. It is also shown that the basic reproduction number of the time-averaged autonomous system is applicable in the case where both the matrix of new infection rate and the matrix of transition and dissipation within infectious compartments are diagonal, but it may underestimate and overestimate infection risks in other cases. The global dynamics of a periodic epidemic model with patch structure is analyzed in order to study the impact of periodic contacts or periodic migrations on the disease transmission.
478 citations
TL;DR: The basic reproduction number and its computation formulae are established for reaction-diffusion epidemic models with compartmental structure and are applied to a spatial model of rabies to study the influence of spatial heterogeneity and population mobility on disease transmission.
Abstract: The theory of the principal eigenvalue is developed for an elliptic eigenvalue problem associated with a linear parabolic cooperative system with some zero diffusion coefficients. Then the basic reproduction number and its computation formulae are established for reaction-diffusion epidemic models with compartmental structure. These theoretical results are applied to a spatial model of rabies to study the influence of spatial heterogeneity and population mobility on disease transmission.
357 citations