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Pulse vaccination strategy in a delayed sir epidemic model with vertical transmission
1.  College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China 
2.  College of Business Administration, Gannan Normal University, Ganzhou 341000, China 
3.  Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, China 
[1] 
Hisashi Inaba. Mathematical analysis of an agestructured SIR epidemic model with vertical transmission. Discrete & Continuous Dynamical Systems  B, 2006, 6 (1) : 6996. doi: 10.3934/dcdsb.2006.6.69 
[2] 
Alan J. Terry. Pulse vaccination strategies in a metapopulation SIR model. Mathematical Biosciences & Engineering, 2010, 7 (2) : 455477. doi: 10.3934/mbe.2010.7.455 
[3] 
Qianqian Cui, Zhipeng Qiu, Ling Ding. An SIR epidemic model with vaccination in a patchy environment. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 11411157. doi: 10.3934/mbe.2017059 
[4] 
C. Connell McCluskey. Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence. Mathematical Biosciences & Engineering, 2010, 7 (4) : 837850. doi: 10.3934/mbe.2010.7.837 
[5] 
Toshikazu Kuniya, Mimmo Iannelli. $R_0$ and the global behavior of an agestructured SIS epidemic model with periodicity and vertical transmission. Mathematical Biosciences & Engineering, 2014, 11 (4) : 929945. doi: 10.3934/mbe.2014.11.929 
[6] 
Masaki Sekiguchi, Emiko Ishiwata, Yukihiko Nakata. Dynamics of an ultradiscrete SIR epidemic model with time delay. Mathematical Biosciences & Engineering, 2018, 15 (3) : 653666. doi: 10.3934/mbe.2018029 
[7] 
Xiaomei Feng, Zhidong Teng, Kai Wang, Fengqin Zhang. Backward bifurcation and global stability in an epidemic model with treatment and vaccination. Discrete & Continuous Dynamical Systems  B, 2014, 19 (4) : 9991025. doi: 10.3934/dcdsb.2014.19.999 
[8] 
Geni Gupur, XueZhi Li. Global stability of an agestructured SIRS epidemic model with vaccination. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 643652. doi: 10.3934/dcdsb.2004.4.643 
[9] 
Aili Wang, Yanni Xiao, Robert A. Cheke. Global dynamics of a piecewise epidemic model with switching vaccination strategy. Discrete & Continuous Dynamical Systems  B, 2014, 19 (9) : 29152940. doi: 10.3934/dcdsb.2014.19.2915 
[10] 
Xia Wang, Shengqiang Liu. Global properties of a delayed SIR epidemic model with multiple parallel infectious stages. Mathematical Biosciences & Engineering, 2012, 9 (3) : 685695. doi: 10.3934/mbe.2012.9.685 
[11] 
Deqiong Ding, Wendi Qin, Xiaohua Ding. Lyapunov functions and global stability for a discretized multigroup SIR epidemic model. Discrete & Continuous Dynamical Systems  B, 2015, 20 (7) : 19711981. doi: 10.3934/dcdsb.2015.20.1971 
[12] 
Jing Hui, Lansun Chen. Impulsive vaccination of sir epidemic models with nonlinear incidence rates. Discrete & Continuous Dynamical Systems  B, 2004, 4 (3) : 595605. doi: 10.3934/dcdsb.2004.4.595 
[13] 
Y. Chen, L. Wang. Global attractivity of a circadian pacemaker model in a periodic environment. Discrete & Continuous Dynamical Systems  B, 2005, 5 (2) : 277288. doi: 10.3934/dcdsb.2005.5.277 
[14] 
Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya. Global stability for a class of discrete SIR epidemic models. Mathematical Biosciences & Engineering, 2010, 7 (2) : 347361. doi: 10.3934/mbe.2010.7.347 
[15] 
Arnaud Ducrot, Michel Langlais, Pierre Magal. Qualitative analysis and travelling wave solutions for the SI model with vertical transmission. Communications on Pure & Applied Analysis, 2012, 11 (1) : 97113. doi: 10.3934/cpaa.2012.11.97 
[16] 
Shangzhi Li, Shangjiang Guo. Permanence and extinction of a stochastic SIS epidemic model with three independent Brownian motions. Discrete & Continuous Dynamical Systems  B, 2021, 26 (5) : 26932719. doi: 10.3934/dcdsb.2020201 
[17] 
Zhen Jin, Zhien Ma. The stability of an SIR epidemic model with time delays. Mathematical Biosciences & Engineering, 2006, 3 (1) : 101109. doi: 10.3934/mbe.2006.3.101 
[18] 
Yan Li, WanTong Li, Guo Lin. Traveling waves of a delayed diffusive SIR epidemic model. Communications on Pure & Applied Analysis, 2015, 14 (3) : 10011022. doi: 10.3934/cpaa.2015.14.1001 
[19] 
Urszula Ledzewicz, Heinz Schättler. On optimal singular controls for a general SIRmodel with vaccination and treatment. Conference Publications, 2011, 2011 (Special) : 981990. doi: 10.3934/proc.2011.2011.981 
[20] 
Jinhu Xu, Yicang Zhou. Global stability of a multigroup model with vaccination age, distributed delay and random perturbation. Mathematical Biosciences & Engineering, 2015, 12 (5) : 10831106. doi: 10.3934/mbe.2015.12.1083 
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