04458nam 2200577 450 991078825720332120220819055056.01-4704-1686-7(CKB)3150000000020200(EBL)3114344(SSID)ssj0001266212(PQKBManifestationID)11738187(PQKBTitleCode)TC0001266212(PQKBWorkID)11249889(PQKB)10848407(MiAaPQ)EBC3114344(RPAM)17934149(PPN)197102611(EXLCZ)99315000000002020020150415h20142014 uy 0engur|n|---|||||txtccrMathematics of continuous and discrete dynamical systems AMS Special Session in Honor of Ronald Mickens's 70th birthday Nonstandard Finite-Difference Discretizations and Nonlinear Oscillations, January 9-10, 2013, San Diego, CA /Abba B. Gumel, editorProvidence, Rhode Island :American Mathematical Society,2014.©20141 online resource (310 p.)Contemporary mathematics,6180271-4132Description based upon print version of record.0-8218-9862-0 Includes bibliographical references at the end of each chapters.Preface -- Biographical Summary of Ronald E. Mickens -- Deterministic and Stochastic SIR Epidemic Models with Power Function Transmission and Recovery Rates -- 1. Introduction -- 2. ODE Model -- 3. CTMC Model -- 4. SDE Model -- 5. Computational Results -- 6. Summary -- Acknowledgments -- References -- Evaluating the Cost-Effectiveness of Vaccination Programs -- 1. Introduction -- 2. Background and modeling framework -- 3. Model extensions and future research -- 4. Summary and concluding remarks -- References -- A Simple Two-Patch Epidemiological Model with Allee Effects and Disease-Modified Fitness -- 1. Introduction -- 2. A two-patch SI model -- 3. Endemic states -- 4. The effects of dispersal -- 5. Discussion -- 6. Proofs -- Acknowledgements -- References -- Designing NSFD Methods for Models of Population Interactions -- 1. Introduction -- 2. Definitions and Preliminaries -- 3. PESN methods for systems with hyperbolic equilibria -- 4. PAESN methods for systems with non-hyperbolic equilibria -- 5. Numerical Simulations -- 6. Discussion and Conclusions -- References -- Nonstandard Discretizations of the SIS Epidemiological Model with and without Diffusion -- 1. Introduction -- 2. Qualitative properties of the model -- 3. Nonstandard Runge-Kutta Method for the SIS Model -- 4. NSFD scheme for the SIS model -- 5. NSFD schemes for SIS-Diffusion Model -- 6. Conclusion -- Acknowledgements -- References -- Galerkin-Least Squares Approximations for Delay Differential Equations: Application to a Circadian Rhythm Model -- 1. Introduction -- 2. Galerkin-Least Squares Approximation -- 3. DDE Model for Circadian Rhythm -- 4. Equilibria and Linear Stability Analysis -- 5. Numerical Simulations -- Conclusions -- Acknowledgements -- References -- Exact Finite Difference Schemes -- 1. Introduction -- 2. Exact Finite Difference Schemes for ODEs -- 3. First-order linear system of two equations -- 4. Exact finite difference schemes for some PDEs -- 5. Discussion -- Acknowledgements -- References -- Design and Analysis of NSFD Methods for the Diffusion-Free Brusselator -- 1. Introduction -- 2. The diffusion-free Brusselator system -- 3. Design of NSFD methods -- 6. Conclusions and perspectives.Contemporary mathematics,6180271-4132Nonlinear oscillationsCongressesDifferential equationsAsymptotic theoryCongressesNonlinear oscillationsDifferential equationsAsymptotic theory515.39234C1534D0534D2034D2337M2039A2839A3092B05mscMickens Ronald E.1943-Gumel Abba B.1966-AMS Special Session in Honor of Ronald Micken's 70th Birthday on Nonstandard Finite-Difference Discretizations and Nonlinear OscillationsMiAaPQMiAaPQMiAaPQBOOK9910788257203321Mathematics of continuous and discrete dynamical systems3855186UNINA