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Volume 35, Issue 3
An SIRS Epidemic Model with Pulse Vaccination, Birth Pulse and Logistic Death Rate

Jianzhong Gao & Tailei Zhang

DOI: 10.13447/j.1674-5647.2019.03.06

Commun. Math. Res., 35 (2019), pp. 247-263.

Published online: 2019-12

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  • Abstract

In this paper, we propose an SIRS epidemic model with pulse vaccination, birth pulse and Logistic death rate. By using the stroboscopic map of a discrete dynamical system, the disease-free periodic solution (DFPS for short) of the model under pulse vaccination and birth pulse is obtained. Based on the Floquet theory and comparison theorem of impulsive differential equations, the global asymptotic stability of the DFPS is given, and sufficient conditions for the permanence of the model are obtained. In addition, numerical simulations are done to confirm our theoretical results. 

  • Keywords

Logistic death rate, birth pulse, threshold value, global stability, permanence

  • AMS Subject Headings

34A37, 34A12, 34A40

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

gaojianzhong2017@126.com (Jianzhong Gao)

t.l.zhang@126.com (Tailei Zhang)

  • BibTex
  • RIS
  • TXT
@Article{CMR-35-247, author = {Gao , Jianzhong and Zhang , Tailei}, title = {An SIRS Epidemic Model with Pulse Vaccination, Birth Pulse and Logistic Death Rate}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {35}, number = {3}, pages = {247--263}, abstract = {

In this paper, we propose an SIRS epidemic model with pulse vaccination, birth pulse and Logistic death rate. By using the stroboscopic map of a discrete dynamical system, the disease-free periodic solution (DFPS for short) of the model under pulse vaccination and birth pulse is obtained. Based on the Floquet theory and comparison theorem of impulsive differential equations, the global asymptotic stability of the DFPS is given, and sufficient conditions for the permanence of the model are obtained. In addition, numerical simulations are done to confirm our theoretical results. 

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2019.03.06}, url = {http://global-sci.org/intro/article_detail/cmr/13530.html} }
TY - JOUR T1 - An SIRS Epidemic Model with Pulse Vaccination, Birth Pulse and Logistic Death Rate AU - Gao , Jianzhong AU - Zhang , Tailei JO - Communications in Mathematical Research VL - 3 SP - 247 EP - 263 PY - 2019 DA - 2019/12 SN - 35 DO - http://doi.org/10.13447/j.1674-5647.2019.03.06 UR - https://global-sci.org/intro/article_detail/cmr/13530.html KW - Logistic death rate, birth pulse, threshold value, global stability, permanence AB -

In this paper, we propose an SIRS epidemic model with pulse vaccination, birth pulse and Logistic death rate. By using the stroboscopic map of a discrete dynamical system, the disease-free periodic solution (DFPS for short) of the model under pulse vaccination and birth pulse is obtained. Based on the Floquet theory and comparison theorem of impulsive differential equations, the global asymptotic stability of the DFPS is given, and sufficient conditions for the permanence of the model are obtained. In addition, numerical simulations are done to confirm our theoretical results. 

Gao , Jianzhong and Zhang , Tailei. (2019). An SIRS Epidemic Model with Pulse Vaccination, Birth Pulse and Logistic Death Rate. Communications in Mathematical Research . 35 (3). 247-263. doi:10.13447/j.1674-5647.2019.03.06
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