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Epidemic models with nonlinear infection forces
1.  Department of Mathematics, Southwest Normal University, Chongqing, 400715, PR, China 
[1] 
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 
[2] 
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 
[3] 
Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595607. doi: 10.3934/mbe.2007.4.595 
[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] 
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 
[6] 
Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya. Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays. Discrete & Continuous Dynamical Systems  B, 2011, 15 (1) : 6174. doi: 10.3934/dcdsb.2011.15.61 
[7] 
Gerardo Chowell, R. Fuentes, A. Olea, X. Aguilera, H. Nesse, J. M. Hyman. The basic reproduction number $R_0$ and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 14551474. doi: 10.3934/mbe.2013.10.1455 
[8] 
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 
[9] 
Jianquan Li, Yicang Zhou, Jianhong Wu, Zhien Ma. Complex dynamics of a simple epidemic model with a nonlinear incidence. Discrete & Continuous Dynamical Systems  B, 2007, 8 (1) : 161173. doi: 10.3934/dcdsb.2007.8.161 
[10] 
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 
[11] 
Chengzhi Li, Jianquan Li, Zhien Ma. Codimension 3 BT bifurcations in an epidemic model with a nonlinear incidence. Discrete & Continuous Dynamical Systems  B, 2015, 20 (4) : 11071116. doi: 10.3934/dcdsb.2015.20.1107 
[12] 
Chengxia Lei, Fujun Li, Jiang Liu. Theoretical analysis on a diffusive SIR epidemic model with nonlinear incidence in a heterogeneous environment. Discrete & Continuous Dynamical Systems  B, 2018, 23 (10) : 44994517. doi: 10.3934/dcdsb.2018173 
[13] 
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 
[14] 
Tom Burr, Gerardo Chowell. The reproduction number $R_t$ in structured and nonstructured populations. Mathematical Biosciences & Engineering, 2009, 6 (2) : 239259. doi: 10.3934/mbe.2009.6.239 
[15] 
Naeem M. H. Alkoumi, Pedro J. Torres. Estimates on the number of limit cycles of a generalized Abel equation. Discrete & Continuous Dynamical Systems  A, 2011, 31 (1) : 2534. doi: 10.3934/dcds.2011.31.25 
[16] 
Jinhu Xu, Yicang Zhou. Global stability of a multigroup model with generalized nonlinear incidence and vaccination age. Discrete & Continuous Dynamical Systems  B, 2016, 21 (3) : 977996. doi: 10.3934/dcdsb.2016.21.977 
[17] 
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 
[18] 
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 
[19] 
Jianhe Shen, Shuhui Chen, Kechang Lin. Study on the stability and bifurcations of limit cycles in higherdimensional nonlinear autonomous systems. Discrete & Continuous Dynamical Systems  B, 2011, 15 (1) : 231254. doi: 10.3934/dcdsb.2011.15.231 
[20] 
Ling Xue, Caterina Scoglio. Networklevel reproduction number and extinction threshold for vectorborne diseases. Mathematical Biosciences & Engineering, 2015, 12 (3) : 565584. doi: 10.3934/mbe.2015.12.565 
2018 Impact Factor: 1.313
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