Global phase portraits of a SIS model

Applied Mathematics and Computation

Volumn 219, Issue 9, 2013, Pages 4924-4930

  Oliveira, Regilene D S ^a   Rezende, Alex C ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Endemic and disease free steady states; Global phase portrait; SIS epidemic model

Indexed keywords

DIFFERENTIAL SYSTEMS; EPIDEMIC MODELS; INFECTIOUS DISEASE; INTEGRABILITY; PHASE PORTRAIT; RE-INFECTION; SIS MODEL; STEADY STATE; SUSCEPTIBLE-INFECTED-SUSCEPTIBLE MODEL; TOPOLOGICAL PHASE;

LEACHING; ORDINARY DIFFERENTIAL EQUATIONS;

TOPOLOGY;

EID: 84871214109     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2012.10.090     Document Type: Review

References (13)

1. W.E. Boyce, and R.C. DiPrima Elementary Differential Equations and Boundary Value Problems 1965 John Wiley & Sons Inc. New York, London-Sydney
2. F. Brauer Basic ideas of mathematical epidemiology C. Castillo-Chavez, S. Blower Sally, P. van den Driessche, D. Kirschner, A.A. Yakubu, Mathematical Approaches for Emerging and Reemerging Infectious Diseases The IMA Volumes in Mathematics and its Applications 2002 Springer-Verlag New York 31 65
3. W.O. Kermack, and A.G. McKendrick A contribution to the mathematical theory of epidemics Proc. R. Soc. Lond. 115 1927 700 721
4. S.A. Levin New directions in the mathematics of infectious diseases C. Castillo-Chavez, S. Blower Sally, P. van den Driessche, D. Kirschner, A.A. Yakubu, Mathematical Approaches for Emerging and Reemerging Infectious Diseases The IMA Volumes in Mathematics and its Applications 2002 Springer-Verlag New York 1 5
5. J. Llibre, and C. Valls Integrability of a SIS model J. Math. Anal. Appl. 344 2008 574 578
6. F. Dumortier, J. Llibre, and J.C. Artés Qualitative Theory of Planar Differential Systems Universitext 2006 Springer Berlin, Heildelberg, NY
7. M.C. Nucci, and P.G.L. Leach An integrable SIS model J. Math. Anal. Appl. 290 2004 506 518
8. D. Schlomiuk, and N. Vulpe Global topological classification of Lotka-Volterra quadratic differential systems Electron. J. Differ. Equat. 64 2012 1 69
9. H. Shi, Z. Duan, and G. Chen An SIS model with infective medium on complex networks Physica A 387 2008 2133 2144
10. C. Vargas-De-Léon Constructions of Lyapunov functions for classic SIS Foro RED-Mat. 26 2009
11. C. Vargas-De-Léon On the global stability of SIS, SIR and SIRS epidemic models with standard incidence Chaos Solitons Fract. 44 2011 1106 1110
12. C. Vargas-De-Léon Stability analysis of a SIS epidemic model with standard incidence Foro RED-Mat. 28 2011
13. P.F. Verhulst Notice sur la loi que la population suit dans son acroissement Corr. Math. Phys. 10 1838 113 121