WebMorris Hirsch, Hal Smith, Xiao‐Qiang Zhao, Chain transitivity, attractivity, and strong repellors for semidynamical systems, J. Dynam. Differential Equations, 13 (2001), 107–131. ... Robust persistence for semidynamical systems, Proceedings of the Third World Congress of Nonlinear Analysts, Part 9 (Catania, 2000), Vol. 47, 2001, 6169–6179. WebApr 2, 2024 · In this paper, we propose an SIS-type reaction-diffusion equations, which contains both direct transmission and indirect transmission via free-living and spatially diffusive bacteria/virus in the contaminated environment, motivated by the dynamics of hospital infections.
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WebWe study the local and global stabilities of the disease-free equilibrium and the uniform persistence. In the case when the diffusion rate of infected individuals is constant, we carry out a bifurcation analysis of equilibria by considering the maximal treatment rate as the bifurcation parameter. WebIt is found that a disease may spread when the population migrates in two patches, even though it dies out in each isolated patch. It is also found that the disease admits multiple exchanges between persistence and extinction for some types of migrations of individuals. Keywords population dispersal infection period reproduction number persistence the boy and the rainbow
Bifurcation Analysis of a Diffusive SIR Model with Saturated …
WebLet M be a compact invariant set contained in a boundary hyperplane of the positive orthant of ℝ n for a discrete or continuous time dynamical system defined on the positive orthant. Using elementary arguments, we show that M is uniformly weakly repelling in directions normal to the boundary in which M resides provided all normal Lyapunov exponents are … WebIf permanence persists under perturbations of the matrices A i ( x), the equations are robustly permanent. We provide sufficient and necessary conditions for robust permanence in terms of Lyapunov exponents for invariant measures supported by the extinction set. Applications to ecological and epidemiological models are given. Keywords Web2.1 SARX System A SARX system is de ned by the following expression: y t= X n a j=1 a j(z t)y t j+ X n c k=1 c k(z t)u t k+ n t (1) 2 the boy and the sea manga