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Mathematical analysis of an agestructured SIR epidemic model with vertical transmission
1.  Department of Mathematical Sciences, University of Tokyo, 381 Komaba Meguroku, Tokyo 1538914, Japan 
[1] 
Shujing Gao, Dehui Xie, Lansun Chen. Pulse vaccination strategy in a delayed sir epidemic model with vertical transmission. Discrete & Continuous Dynamical Systems  B, 2007, 7 (1) : 7786. doi: 10.3934/dcdsb.2007.7.77 
[2] 
Andrea Franceschetti, Andrea Pugliese, Dimitri Breda. Multiple endemic states in agestructured $SIR$ epidemic models. Mathematical Biosciences & Engineering, 2012, 9 (3) : 577599. doi: 10.3934/mbe.2012.9.577 
[3] 
Toshikazu Kuniya, Jinliang Wang, Hisashi Inaba. A multigroup SIR epidemic model with age structure. Discrete & Continuous Dynamical Systems  B, 2016, 21 (10) : 35153550. doi: 10.3934/dcdsb.2016109 
[4] 
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 
[5] 
Toshikazu Kuniya, Yoshiaki Muroya, Yoichi Enatsu. Threshold dynamics of an SIR epidemic model with hybrid of multigroup and patch structures. Mathematical Biosciences & Engineering, 2014, 11 (6) : 13751393. doi: 10.3934/mbe.2014.11.1375 
[6] 
Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete & Continuous Dynamical Systems  B, 2013, 18 (1) : 3756. doi: 10.3934/dcdsb.2013.18.37 
[7] 
Dimitri Breda, Stefano Maset, Rossana Vermiglio. Numerical recipes for investigating endemic equilibria of agestructured SIR epidemics. Discrete & Continuous Dynamical Systems  A, 2012, 32 (8) : 26752699. doi: 10.3934/dcds.2012.32.2675 
[8] 
Liang Zhang, ZhiCheng Wang. Threshold dynamics of a reactiondiffusion epidemic model with stage structure. Discrete & Continuous Dynamical Systems  B, 2017, 22 (10) : 37973820. doi: 10.3934/dcdsb.2017191 
[9] 
BinGuo Wang, WanTong Li, Liang Zhang. An almost periodic epidemic model with age structure in a patchy environment. Discrete & Continuous Dynamical Systems  B, 2016, 21 (1) : 291311. doi: 10.3934/dcdsb.2016.21.291 
[10] 
Liming Cai, Maia Martcheva, XueZhi Li. Epidemic models with age of infection, indirect transmission and incomplete treatment. Discrete & Continuous Dynamical Systems  B, 2013, 18 (9) : 22392265. doi: 10.3934/dcdsb.2013.18.2239 
[11] 
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 
[12] 
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 
[13] 
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 
[14] 
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 
[15] 
John Cleveland. Basic stage structure measure valued evolutionary game model. Mathematical Biosciences & Engineering, 2015, 12 (2) : 291310. doi: 10.3934/mbe.2015.12.291 
[16] 
WanTong Li, Guo Lin, Cong Ma, FeiYing Yang. Traveling wave solutions of a nonlocal delayed SIR model without outbreak threshold. Discrete & Continuous Dynamical Systems  B, 2014, 19 (2) : 467484. doi: 10.3934/dcdsb.2014.19.467 
[17] 
Zhenguo Bai. Threshold dynamics of a periodic SIR model with delay in an infected compartment. Mathematical Biosciences & Engineering, 2015, 12 (3) : 555564. doi: 10.3934/mbe.2015.12.555 
[18] 
Jacek Banasiak, Eddy Kimba Phongi, MirosŁaw Lachowicz. A singularly perturbed SIS model with age structure. Mathematical Biosciences & Engineering, 2013, 10 (3) : 499521. doi: 10.3934/mbe.2013.10.499 
[19] 
Jinliang Wang, Xianning Liu, Toshikazu Kuniya, Jingmei Pang. Global stability for multigroup SIR and SEIR epidemic models with agedependent susceptibility. Discrete & Continuous Dynamical Systems  B, 2017, 22 (7) : 27952812. doi: 10.3934/dcdsb.2017151 
[20] 
Nguyen Huu Du, Nguyen Thanh Dieu. Longtime behavior of an SIR model with perturbed disease transmission coefficient. Discrete & Continuous Dynamical Systems  B, 2016, 21 (10) : 34293440. doi: 10.3934/dcdsb.2016105 
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