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The effect of integral conditions in certain equations modelling epidemics and population growth. (English) Zbl 0464.92022


MSC:

92D25 Population dynamics (general)
34K20 Stability theory of functional-differential equations

Citations:

Zbl 0384.92013
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Full Text: DOI

References:

[1] Bellman, R., Cooke, K.: Differential-difference equations. New York: Academic Press 1963 · Zbl 0105.06402
[2] Busenberg, S., Cooke, K.: Periodic solutions of a periodic non-linear delay differential equation. SIAM J. Applied Math. 35, 704-721 (1978) · Zbl 0391.34022 · doi:10.1137/0135059
[3] Cooke, K., Yorke, J.: Some equations modelling growth processes and gonorrhea epidemics. Math. Biosciences 16, 75-101 (1973) · Zbl 0251.92011 · doi:10.1016/0025-5564(73)90046-1
[4] Cooke, K.: Stability analysis for a vector disease model. Rocky Mountain Math. J., 9, 31-42 (1979) · Zbl 0423.92029 · doi:10.1216/RMJ-1979-9-1-31
[5] Cooke, K.: Functional-differential equations: Some models and perturbation problems. Differential equations and dynamical systems, pp. 167-183. New York: Academic Press 1967 · Zbl 0189.40301
[6] Green, D.: Self-oscillations for epidemic models. Math. Biosciences 38, 91-111 (1978) · Zbl 0384.92013 · doi:10.1016/0025-5564(78)90020-2
[7] Grossman, Z.: Oscillatory phenomena in a model of infectious diseases, preprint · Zbl 0457.92020
[8] Hale, J.: Behavior near constant solutions of functional differential equations. J. Diff. Eq. 15, 278-294 (1974) · Zbl 0273.34049 · doi:10.1016/0022-0396(74)90080-1
[9] Hale, J.: Theory of functional differential equations. New York: Springer 1977 · Zbl 0352.34001
[10] Hoppensteadt, F., Waltman, P.: A problem in the theory of epidemics. Math. Biosciences 9, 71-91 (1970) · Zbl 0212.52105 · doi:10.1016/0025-5564(70)90094-5
[11] Hoppensteadt, F.: Mathematical theories of populations: Demographics, genetics and epidemics, Philadelphia: SIAM 1975 · Zbl 0304.92012
[12] Seifert, G.: Positively invariant closed sets for systems of delay differential equations. J. Diff. Eq. 22, 292-304 (1976) · Zbl 0332.34068 · doi:10.1016/0022-0396(76)90029-2
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