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 - <p style="text-align: justify;">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.&nbsp;</p>