Global stability of an age-structured SIRS epidemic model with vaccination

Discrete and Continuous Dynamical Systems - Series B

Volumn 4, Issue 3, 2004, Pages 643-652

  Li, Xue Zhi ^a   Gupur, Geni ^b  

^a XINYANG NORMAL UNIVERSITY   (China)

^b XINJIANG UNIVERSITY   (China)

Author keywords

Age structured SIRS epidemic model; Endemic state; Global stability; Infection free steady state; Reproductive number; Vaccination

Indexed keywords

EID: 2942677424     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2004.4.643     Document Type: Conference Paper

References (14)

1. D.Greenhalgh, ANALYTICAL RESULTS ON THE STABILITY OF AGE STRUCTURED EPIDEMIC MODEL, IMA J.Math.Appl.Med.Biol., 4(1987), 109-144.
2. D.Greenhalgh, ANALYTICAL THRESHOLD AND STABILITY RESULTS ON AGE-STRUCTURED EPIDEMIC MODELS WITH VACCINATION, Theor. Popul. Biol., 33(1988), 266-290.
3. H.Inaba, THRESHOLD AND STABILITY RESULTS FOR AN AGE-STRUCTURED EPIDEMIC MODEL, J. Math. Biol., 28(1990), 149-175.
4. Y.Cha, M.Iannelli and E.Milner, EXISTENCE AND UNIQUENESS OF ENDEMIC STATES FOR THE AGE-STRUCTURED SIR EPIDEMIC MODEL, Math. Biosci., 150(1998), 177-190.
5. J.Müller, OPTIMAL VACCINATION PARTTERNS IN AGE-STRUCTURED POPULATION, SIAM J.Appl. Math., 59(1998), 222-241.
6. J.Müller, OPTIMAL VACCINATION PARTTERNS IN AGE-STRUCTURED POPULATION: ENDEMIC CASES, Mathematical and Computer Modelling, 31(2000), 149-160.
7. K.P.Hadeler and J. Müller, VACCINATION IN AGE-STRUCTURED POPULATIONS II: OPTIMAL STRATEGIES, in Models for Infectious Human Diseases: Their Structure and Relation to Data. V. Ishan and G. Medley, eds., Cambridge Univ. Press, Cambridge, 1993, 102-114.
8. C.Castillo-Charez and Zhilan Feng, To TREAT OR NOT TO TREAT: THE CASE OF TUBERCULOSIS. J. Math. Biol., 35(1997), 629-645.
9. C. Castillo-Chavez and Zhilan Feng, GLOBLE STABILITY OF AN AGE-STRUCTURED MODEL FOR TB AND ITS APPLICATIONS TO OPTIMAL VACCINATION STRATEGIES, Mathematical Biosciences, 151(1998), 135-154.
10. K.P.Hadeler and J. Müller, VACCINATION IN AGE-STRUCTURED POPULATION I: THE REPRODUCTION NUMBER, in Models for Infectious Human Diseases: Their Structure and Relation to Data. V. Ishan and G. Medley, eds., Cambridge Univ. Press, Cambridge, 1993, 90-101.
11. G.F.Webb, Theory of Nonlinear Age-Dependent Population Dynamics, New York and Basel: Marcel Dekker, 1985.
12. G.Gripenberg S.O.Londen, O.Slaffans, Volterra Integral and Functional Equations, Cambridge University, Cambridge, 1990.
13. Yukio Kan-On, GLOBAL BIFURCATION STRUCTURE OF STATIONARY SOLUTIONS FOR A LOTKA-VOLTERRA COMPETITION MODEL, Discrete and Continuous Dynamical Systems, Series-B, 8(1)(2002), 147-162.
14. Huijiang Zhao, LARGE TIME DECAY ESTIMATES OF SOLUTIONS OF NONLINEAR PARABOLIC EQUATIONS, Discrete and Continuous Dynamical Systems, Series-B, 8(1)(2002), 69-114.