×

A delayed epidemic model with pulse vaccination. (English) Zbl 1149.92329

Summary: A delayed SEIRS epidemic model with pulse vaccination and nonlinear incidence rate is proposed. We analyze the dynamical behaviors of this model and point out that there exists an infection-free periodic solution which is globally attractive if \(R_{1}<1\), \(R_{2}>1\), and the disease is permanent. Our results indicate that a short period of pulse or a large pulse vaccination rate is the sufficient condition for the eradication of the disease. The main feature of this paper is to introduce time delay and impulse into the SEIRS model and give pulse vaccination strategies.

MSC:

92D30 Epidemiology
34K45 Functional-differential equations with impulses
34K60 Qualitative investigation and simulation of models involving functional-differential equations
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] DOI: 10.1016/j.chaos.2006.04.061 · Zbl 1152.34379 · doi:10.1016/j.chaos.2006.04.061
[2] Bulletin of Mathematical Biology 60 pp 1123– (1998) · Zbl 0941.92026 · doi:10.1016/S0092-8240(98)90005-2
[3] DOI: 10.1016/j.chaos.2004.11.062 · Zbl 1065.92046 · doi:10.1016/j.chaos.2004.11.062
[4] DOI: 10.1007/s002850050051 · Zbl 0865.92019 · doi:10.1007/s002850050051
[5] DOI: 10.1016/S0893-9659(01)00153-7 · Zbl 1015.92033 · doi:10.1016/S0893-9659(01)00153-7
[6] DOI: 10.1016/j.amc.2006.07.124 · Zbl 1111.92049 · doi:10.1016/j.amc.2006.07.124
[7] DOI: 10.1137/S0036144500371907 · Zbl 0993.92033 · doi:10.1137/S0036144500371907
[8] (1982)
[9] (1991)
[10] How dose transmisson depend on population size pp 84– (1995)
[11] DOI: 10.1007/BF00276956 · Zbl 0582.92023 · doi:10.1007/BF00276956
[12] (1993)
[13] DOI: 10.1007/s00285-003-0243-5 · Zbl 1058.92051 · doi:10.1007/s00285-003-0243-5
[14] DOI: 10.1016/j.mcm.2003.12.011 · Zbl 1112.34052 · doi:10.1016/j.mcm.2003.12.011
[15] Nonlinear Analysis. Theory, Methods & Applications 52 (3) pp 725– (2003) · Zbl 1027.34086 · doi:10.1016/S0362-546X(02)00129-3
[16] Mathematics in Science and Engineering 191 pp xii+398– (1993)
[17] Series in Modern Applied Mathematics 6 pp xii+273– (1989)
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.