zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Stability of periodic solutions for an SIS model with pulse vaccination. (English) Zbl 1045.92042
Summary: Pulse vaccination is an important strategy for the elimination of infectious diseases. A mathematical SIS model with pulse vaccination is formulated in this paper. The dynamical behavior of the model is studied, and the basic reproductive number $R_0$ is defined. It is proved that the disease-free periodic solution is stable if $R_0 < 1$, and is unstable if $R_0 > 1$. The global stability of the disease-free periodic solution is studied and a sufficient condition is obtained. The existence and stability of endemic periodic solutions are investigated analytically and numerically.

MSC:
92D30Epidemiology
34C25Periodic solutions of ODE
34D23Global stability of ODE
34D05Asymptotic stability of ODE
WorldCat.org
Full Text: DOI
References:
[1] Braur, F.: Basical ideal of mathematical epidemiology. Mathematical approaches for emerging and reemerging infectious diseases 125, 31-65 (2002)
[2] Bailey, N. T. J.: The mathematical theory of infectious diseases. (1975) · Zbl 0334.92024
[3] Capasso, V.: Second edition mathematical structures of epidemic systems, volume 97, lectures notes in biomathematics. Mathematical structures of epidemic systems, volume 97, lectures notes in biomathematics (1993) · Zbl 0798.92024
[4] Hethcote, H. W.: Mathematics of infectious diseases. SIAM review 42, No. 4, 599-653 (2000) · Zbl 0993.92033
[5] Hethcote, H. W.: Three basic epidemic models. Applied mathematical ecology, 119-144 (1989)
[6] Kribs-Zaleta, C. M.; Valesco-Hernández, J. X.: A simple vaccination model with multiple endemic states. Mathematical biosciences 164, No. 2, 183-201 (2000) · Zbl 0954.92023
[7] Nokes, D. J.; Swinton, J.: The control of childhood viral infections by pulse vaccination. IMA journal of mathematics applied in medicine & biology 12, 29-53 (1995) · Zbl 0832.92024
[8] Stone, L.; Shulgin, B.; Agur, Z.: Theoretical examination of the pulse vaccination policy in the SIR epidemic modelc. Mathl. comput. Modelling 31, No. 4/5, 207-215 (2000) · Zbl 1043.92527
[9] D’onofrio, A.: Pulse vaccination strategy in the SIR epidemic model: global asymptotic stable eradication in presence of vaccine failures. Mathl. comput. Modelling 36, No. 4/5, 473-489 (2002) · Zbl 1025.92011
[10] D’onofrio, A.: Stability properties of pulse vaccination strategy in SEIR epidemic model. Mathematical biosciences 179, No. 1, 57-72 (2002) · Zbl 0991.92025
[11] Lakshmikantham, V.; Bailov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations. (1989) · Zbl 0719.34002
[12] Bailov, D. D.; Simeonov, P. S.: The stability theory of impulsive differential equations, asymptotic properties of the solutions. (1995)
[13] Lasalle, J. P.: The stability of dynamical systems. (1976) · Zbl 0364.93002