El-Doma, M. Stability analysis for a general age-dependent vaccination model. (English) Zbl 0894.92027 Math. Comput. Modelling 24, No. 7, 109-117 (1996). Summary: An SIR epidemic model of a general age-dependent vaccination model is investigated when the fertility, mortality and removal rates depend on age. We give threshold criteria for the existence of equilibriums and perform stability analysis. Furthermore, a critical vaccination coverage that is sufficient to eradicate the disease is determined. Cited in 2 Documents MSC: 92D30 Epidemiology 45K05 Integro-partial differential equations 45M10 Stability theory for integral equations Keywords:age-structure; nonlinear equations; SIR epidemic model; age-dependent vaccination model; threshold criteria PDFBibTeX XMLCite \textit{M. El-Doma}, Math. Comput. Modelling 24, No. 7, 109--117 (1996; Zbl 0894.92027) Full Text: DOI References: [1] Hethcote, H. W., Review and Commentary: Measles and rubella in the United States, American Journal of Epidemiology, 117, 1, 2-13 (1983) [2] Katzmann, W.; Dietz, K., Evaluation of age-specific vaccination stategies, Theor. Population Biology, 25, 125-137 (1984) · Zbl 0544.92023 [3] Anderson, R. M.; May, R. M., Directly transmitted infectious diseases: Control by vaccination, Science, 215, 1053-1060 (1982) · Zbl 1225.37099 [4] Busenberg, S. N.; Cooke, K. L.; Iannelli, M., Endemic threshold stability in a class of age-structured epidemics, SIAM J. Appl. Math., 48, 6, 1379-1395 (1988) · Zbl 0666.92013 [5] M. El-Doma, Analysis of an age-dependent vaccination model, preprint.; M. El-Doma, Analysis of an age-dependent vaccination model, preprint. · Zbl 1228.92070 [6] M. El-Doma, Stability analysis for an age-dependent vaccination model, preprint, (to appear).; M. El-Doma, Stability analysis for an age-dependent vaccination model, preprint, (to appear). [7] M. El-Doma, Analysis of an age-dependent vaccination model for a vertically transmitted disease, preprint, (to appear).; M. El-Doma, Analysis of an age-dependent vaccination model for a vertically transmitted disease, preprint, (to appear). [8] M. El-Doma, Analysis of a general age-dependent vaccination model, preprint.; M. El-Doma, Analysis of a general age-dependent vaccination model, preprint. [9] El-Doma, M., Analysis of nonlinear integro-differential equations arising in age-dependent epidemic models, Nonlinear Analysis, Theory, Methods and Applications, 11, 913-937 (1987) · Zbl 0633.45008 [10] Bellman, R.; Cooke, K. L., Differential-Difference Equations (1963), Academic Press: Academic Press New York · Zbl 0118.08201 [11] Hoppensteadt, F., Mathematical theory of population demographics, genetics and epidemics, (Presented at the CBMS-NSF Regional Conference in Applied Mathematics. Presented at the CBMS-NSF Regional Conference in Applied Mathematics, Philadelphia (1975)) · Zbl 0304.92012 [12] Feller, W., On the integral equation of renewal theory, Ann. Math. Stat., 12, 243-267 (1941) · JFM 67.0370.02 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.