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On pulse vaccination strategy in the SIR epidemic model with vertical transmission. (English) Zbl 1064.92041
Summary: The aim of this short paper is to improve a result recently given by {\it Z. Lu} et al. [Math. Comput. Modelling 36, No. 9--10, 1039--1057 (2002; Zbl 1023.92026)] on the global asymptotic stability of the eradication solution of the pulse vaccination strategy applied to diseases with vertical transmission, by demonstrating that the condition for local stability guarantees also the global stability.

MSC:
92D30Epidemiology
34A37Differential equations with impulses
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Full Text: DOI
References:
[1] Lu, Z.; Chi, X.; Chen, L.: The effect of constant and pulse vaccination on SIR epidemic model with horizontal and vertical transmission. Math. comput. Modelling 36, 1039-1057 (2002) · Zbl 1023.92026
[2] Shulgin, B.; Stone, L.; Agur, Z.: Theoretical examination of pulse vaccination policy in the SIR epidemic model. Math. comput. Modelling 31, No. 4--5, 207-215 (2000) · Zbl 1043.92527
[3] Agur, Z.; Cojocaru, L.; Mazor, G.; Anderson, R. M.; Danon, Y. L.: Pulse mass measles vaccination across age cohorts. Proc. natl. Acad. sci. USA 90, 11698-11702 (1993)
[4] Shulgin, B.; Stone, L.; Agur, Z.: Pulse vaccination strategy in the SIR epidemic model. Bull. math. Biol. 60, 1123-1148 (1998) · Zbl 0941.92026
[5] D’onofrio, A.: Pulse vaccination strategy in SIR epidemic model: global stability, vaccine failures and double vaccinations. Math. comput. Modelling 36, No. 4--5, 461-478 (2002)
[6] D’onofrio, A.: Stability property of pulse vaccination technique in SEIR epidemic model. Math. biosci. 179, No. 1, 57-72 (2002)
[7] D’onofrio, A.: Mixed pulse vaccination strategy in epidemic model with realistically distributed infectious and latent times. Appl. math. Comput. 151, No. 1 (2004)
[8] Busenberg, S.; Cooke, K.: Vertically transmitted diseases. (1992) · Zbl 0512.92017
[9] Capasso, V.: Mathematical structure of epidemic models. (1993) · Zbl 0798.92024