Stability of disease free sets in epidemic models

Mathematical and Computer Modelling

Volumn 43, Issue 11-12, 2006, Pages 1357-1366

  Laukó, István G ^a  

^a UNIVERSITY OF WISCONSIN MILWAUKEE   (United States)

Author keywords

Asymptotic analysis; Disease free subsets; Epidemic models; Stability

Indexed keywords

LYAPUNOV METHODS; MATHEMATICAL MODELS; SET THEORY;

ASYMPTOTIC ANALYSIS; DISEASE FREE SUBSETS; EPIDEMIC MODELS;

DISEASE CONTROL;

EID: 33646139171     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2005.06.011     Document Type: Article

References (14)

1. Hethcote H.W. The mathematics of infectious diseases. SIAM Review 42 (2000) 599-653
2. Venturino E. The influence of diseases on Lotka-Volterra systems. Rocky Mountain Journal of Mathematics 24 (1994) 381-402
3. Arino J., and van den Driessche P. The basic reproduction number in a multi-city compartmental epidemic model. In: Benvenuti L., De Santis A., and Farina L. (Eds). Positive Systems. LNCIS vol. 294 (2003), Springer-Verlag, Berlin 135-142
4. van den Driessche P., and Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences 180 (2002) 525-540
5. Miroshnik I.V. Partial stability and geometric problems of nonlinear dynamics. Automation and Remote Control 63 (2002) 1730-1744
6. Fradkov A.L., Miroshnik I.V., and Nikiforov V.O. Nonlinear and Adaptive Control of Complex Systems (1999), Kluwer Acad. Publ., Dordrecht
7. Ryashko L.B., and Schnol E.E. On exponentially attracting invariant manifolds of ODEs. Nonlinearity 16 (2003) 147-160
8. Zubov V.I. Mathematical Theory of the Motion Stability (1997), Stock Corp. Mobilnost Plus, St. Petersburg
9. Byrnes C.I. Toward a nonequilibrium theory for nonlinear control systems. Nonlinear Control in the year 2000, vol. 1 (Paris). Lecture Notes in Control and Infrom. Sci. vol. 258 (2001), Springer, London 253-275
10. Miller R.K., and Michel A.N. Ordinary Differential Equations (1982), Academic Press
11. Hethcote H.W., and Ark J.W.V. Epidemiological models for heterogeneous populations: proportionate mixing, parameter estimation and immunization programs. Mathematical Biosciences 84 (1987) 85-118
12. Coddington E.A., and Levinson N. Theory of Ordinary Differential Equations (1955), McGraw Hill
13. Chattopadhyay J., and Arino O. A predator-prey model with disease in the prey. Nonlinear Analysis 36 (1999) 747-766
14. Brown M. Differential Equations and Their Applications. 4th edition (1993), Sringer, New York