Bistable Waves in an Epidemic Model

abstractThe existence, uniqueness up to translation and global exponential stability with phase shift of bistable travelling waves are established for a quasimonotone reaction–diffusion system modelling man–environment–man epidemics. The methods involve phase space investigation, monotone semiflows approach and spectrum analysis.

[1]  E. Coddington,et al.  Theory of Ordinary Differential Equations , 1955 .

[2]  Karl Kunisch,et al.  A reaction-diffusion system arising in modelling man-environment diseases , 1988 .

[3]  Robert A. Gardner Existence and stability of travelling wave solutions of competition models: A degree theoretic approach , 1982 .

[4]  V. Capasso,et al.  A mathematical model for the 1973 cholera epidemic in the European Mediterranean region. , 1979, Revue d'epidemiologie et de sante publique.

[5]  V. Capasso Mathematical Structures of Epidemic Systems , 1993, Lecture Notes in Biomathematics.

[6]  Xiao-Qiang Zhao,et al.  Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models , 2003 .

[7]  V. Volpert,et al.  Location of spectrum and stability of solutions for monotone parabolic system , 1997, Advances in Differential Equations.

[8]  Jifa Jiang,et al.  Saddle-point behavior for monotone semiflows and reaction–diffusion models☆ , 2004 .

[9]  V Capasso,et al.  Convergence to equilibrium states for a reaction-diffusion system modelling the spatial spread of a class of bacterial and viral diseases , 1981, Journal of mathematical biology.

[10]  Xinfu Chen,et al.  Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations , 1997, Advances in Differential Equations.

[11]  C. Conley,et al.  An application of the generalized Morse index to travelling wave solutions of a competitive reaction-diffusion model , 1984 .

[12]  Hal L. Smith,et al.  Abstract functional-differential equations and reaction-diffusion systems , 1990 .

[13]  Peter W. Bates,et al.  Invariant Manifolds for Semilinear Partial Differential Equations , 1989 .

[14]  John Evans,et al.  Nerve Axon Equations: II Stability at Rest , 1972 .

[15]  Vincenzo Capasso,et al.  Analysis of a Reaction-Diffusion System Modeling Man-Environment-Man Epidemics , 1997, SIAM J. Appl. Math..

[16]  Klaus W. Schaaf Asymptotic behavior and traveling wave solutions for parabolic functional-differential equations , 1987 .

[17]  Xiao-Qiang Zhao,et al.  Fisher waves in an epidemic model , 2004 .

[18]  Konstantin Mischaikow,et al.  Travelling waves for mutualist species , 1993 .

[19]  Hal L. Smith,et al.  Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .

[20]  Wenzhang Huang,et al.  Uniqueness of the Bistable Traveling Wave for Mutualist Species , 2001 .

[21]  J. Alexander,et al.  A topological invariant arising in the stability analysis of travelling waves. , 1990 .

[22]  J. Roquejoffre,et al.  Global stability of traveling fronts and convergence towards stacked families of waves in monotone parabolic systems , 1996 .

[23]  Vitaly Volpert,et al.  Traveling Wave Solutions of Parabolic Systems , 1994 .

[24]  Daniel B. Henry Geometric Theory of Semilinear Parabolic Equations , 1989 .

[25]  Xiao-Qiang Zhao,et al.  Dynamical systems in population biology , 2003 .