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)
Integral equation models for endemic infectious diseases. (English) Zbl 0433.92026
MSC:
92D25Population dynamics (general)
45E10Integral equations of the convolution type
References:
[1]Bailey, N. T. J.: The Mathematical Theory of Infectious Diseases, Second Edition. New York: Hafner Press, 1975
[2]Birkhoff, G., Rota, G-C.: Ordinary Differential Equations, Second Edition. New York: John Wiley, 1969
[3]Cooke, K. L., Yorke, J. A.: Some equations modelling growth processes and gonorrhea epidemics. Math. Biosci. 16, 75-101 (1973) · Zbl 0251.92011 · doi:10.1016/0025-5564(73)90046-1
[4]Hale, J. K.: Ordinary Differential Equations. New York: Wiley-Interscience, 1969
[5]Grossman, Z.: Oscillatory phenomena in a model of infectious diseases, preprint
[6]Hethcote, H. W.: Asymptotic behavior and stability in epidemic models. In: Mathematical Problems in Biology, pp. 83-92. Lecture Notes in Biomathematics 2, New York: Springer, 1974
[7]Hethcote, H. W.: Qualitative analyses of communicable disease models. Math. Biosci. 28, 335-356 (1976) · Zbl 0326.92017 · doi:10.1016/0025-5564(76)90132-2
[8]Hethcote, H. W.: An immunization model for a heterogeneous population. Theor. Pop. Biol. 14, 338-349 (1978) · Zbl 0392.92009 · doi:10.1016/0040-5809(78)90011-4
[9]Hethcote, H. W., Stech, H. W., van den Driessche, P.: Nonlinear oscillations in epidemic models, preprint.
[10]Hethcote, H. W., Waltman, P.: Optimal vaccination schedules in a deterministic epidemic model. Math. Biosci. 18, 365-382 (1973) · Zbl 0266.92011 · doi:10.1016/0025-5564(73)90011-4
[11]Hoppensteadt, F.: Mathematical Theories of Populations: Demographics, Genetics and Epidemics. Philadelphia: Society for Industrial and Applied Mathematics, 1975
[12]Hoppensteadt, F., Waltman, P.: A problem in the theory of epidemics II. Math. Biosci 12, 133-145 (1971) · Zbl 0226.92011 · doi:10.1016/0025-5564(71)90078-2
[13]Kermack, W. O., McKendrick, A. G.: Contributions to the mathematical theory of epidemics, part I. Proc. Roy. Soc., Ser. A 115, 700-721 (1927) · doi:10.1098/rspa.1927.0118
[14]Lajmanovich, A., Yorke, J. A.: A deterministic model for gonorrhea in a nonhomogeneous population. Math. Biosci. 28, 221-236 (1976) · Zbl 0344.92016 · doi:10.1016/0025-5564(76)90125-5
[15]Ludwig, D.: Final size distributions for epidemics. Math. Biosci. 23, 33-46 (1975) · Zbl 0318.92025 · doi:10.1016/0025-5564(75)90119-4
[16]Miller, R. K.: On the linearization of Volterra integral equations. J. Math. Anal. Appl. 23, 198-208 (1968) · Zbl 0167.40902 · doi:10.1016/0022-247X(68)90127-3
[17]Miller, R. K.: Nonlinear Volterra Integral Equations. Menlo Park: Benjamin, 1971
[18]Tudor, D. W.: Disease transmission and control in an age structured population, Ph.D. Thesis. University of Iowa, 1979
[19]Waltman, P.: Deterministic Threshold Models in the Theory of Epidemics. Lecture Notes in Biomathematics 1, New York: Springer, 1974
[20]Wang, F. J. S.: Asymptotic behavior of some deterministic epidemic models. SIAM J. Math. Anal. 9, 529-534 (1978) · Zbl 0417.92020 · doi:10.1137/0509034