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Influence of latent period and nonlinear incidence rate on the dynamics of SIRS epidemiological models
1.  Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China 
[1] 
Zhixing Hu, Ping Bi, Wanbiao Ma, Shigui Ruan. Bifurcations of an SIRS epidemic model with nonlinear incidence rate. Discrete & Continuous Dynamical Systems  B, 2011, 15 (1) : 93112. doi: 10.3934/dcdsb.2011.15.93 
[2] 
Yoshiaki Muroya, Toshikazu Kuniya, Yoichi Enatsu. Global stability of a delayed multigroup SIRS epidemic model with nonlinear incidence rates and relapse of infection. Discrete & Continuous Dynamical Systems  B, 2015, 20 (9) : 30573091. doi: 10.3934/dcdsb.2015.20.3057 
[3] 
Hui Miao, Zhidong Teng, Chengjun Kang. Stability and Hopf bifurcation of an HIV infection model with saturation incidence and two delays. Discrete & Continuous Dynamical Systems  B, 2017, 22 (6) : 23652387. doi: 10.3934/dcdsb.2017121 
[4] 
Shouying Huang, Jifa Jiang. Global stability of a networkbased SIS epidemic model with a general nonlinear incidence rate. Mathematical Biosciences & Engineering, 2016, 13 (4) : 723739. doi: 10.3934/mbe.2016016 
[5] 
Yu Ji, Lan Liu. Global stability of a delayed viral infection model with nonlinear immune response and general incidence rate. Discrete & Continuous Dynamical Systems  B, 2016, 21 (1) : 133149. doi: 10.3934/dcdsb.2016.21.133 
[6] 
Yu Yang, Yueping Dong, Yasuhiro Takeuchi. Global dynamics of a latent HIV infection model with general incidence function and multiple delays. Discrete & Continuous Dynamical Systems  B, 2019, 24 (2) : 783800. doi: 10.3934/dcdsb.2018207 
[7] 
Attila Dénes, Gergely Röst. Global stability for SIR and SIRS models with nonlinear incidence and removal terms via Dulac functions. Discrete & Continuous Dynamical Systems  B, 2016, 21 (4) : 11011117. doi: 10.3934/dcdsb.2016.21.1101 
[8] 
Hong Yang, Junjie Wei. Global behaviour of a delayed viral kinetic model with general incidence rate. Discrete & Continuous Dynamical Systems  B, 2015, 20 (5) : 15731582. doi: 10.3934/dcdsb.2015.20.1573 
[9] 
Fabien Crauste. Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model. Mathematical Biosciences & Engineering, 2006, 3 (2) : 325346. doi: 10.3934/mbe.2006.3.325 
[10] 
Pengmiao Hao, Xuechen Wang, Junjie Wei. Global Hopf bifurcation of a population model with stage structure and strong Allee effect. Discrete & Continuous Dynamical Systems  S, 2017, 10 (5) : 973993. doi: 10.3934/dcdss.2017051 
[11] 
Yanan Zhao, Yuguo Lin, Daqing Jiang, Xuerong Mao, Yong Li. Stationary distribution of stochastic SIRS epidemic model with standard incidence. Discrete & Continuous Dynamical Systems  B, 2016, 21 (7) : 23632378. doi: 10.3934/dcdsb.2016051 
[12] 
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 
[13] 
Yu Ji. Global stability of a multiple delayed viral infection model with general incidence rate and an application to HIV infection. Mathematical Biosciences & Engineering, 2015, 12 (3) : 525536. doi: 10.3934/mbe.2015.12.525 
[14] 
Ting Guo, Haihong Liu, Chenglin Xu, Fang Yan. Global stability of a diffusive and delayed HBV infection model with HBV DNAcontaining capsids and general incidence rate. Discrete & Continuous Dynamical Systems  B, 2018, 23 (10) : 42234242. doi: 10.3934/dcdsb.2018134 
[15] 
Jinling Zhou, Yu Yang. Traveling waves for a nonlocal dispersal SIR model with general nonlinear incidence rate and spatiotemporal delay. Discrete & Continuous Dynamical Systems  B, 2017, 22 (4) : 17191741. doi: 10.3934/dcdsb.2017082 
[16] 
Yukihiko Nakata, Yoichi Enatsu, Yoshiaki Muroya. On the global stability of an SIRS epidemic model with distributed delays. Conference Publications, 2011, 2011 (Special) : 11191128. doi: 10.3934/proc.2011.2011.1119 
[17] 
Yuming Chen, Junyuan Yang, Fengqin Zhang. The global stability of an SIRS model with infection age. Mathematical Biosciences & Engineering, 2014, 11 (3) : 449469. doi: 10.3934/mbe.2014.11.449 
[18] 
Yoichi Enatsu, Yukihiko Nakata. Stability and bifurcation analysis of epidemic models with saturated incidence rates: An application to a nonmonotone incidence rate. Mathematical Biosciences & Engineering, 2014, 11 (4) : 785805. doi: 10.3934/mbe.2014.11.785 
[19] 
Qun Liu, Daqing Jiang, Tasawar Hayat, Ahmed Alsaedi. Dynamical behavior of a multigroup SIRS epidemic model with standard incidence rates and Markovian switching. Discrete & Continuous Dynamical Systems  A, 2019, 39 (10) : 56835706. doi: 10.3934/dcds.2019249 
[20] 
Yasuhito Miyamoto. Global bifurcation and stable twophase separation for a phase field model in a disk. Discrete & Continuous Dynamical Systems  A, 2011, 30 (3) : 791806. doi: 10.3934/dcds.2011.30.791 
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