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Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic
1.  Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada 
[1] 
Mahin Salmani, P. van den Driessche. A model for disease transmission in a patchy environment. Discrete & Continuous Dynamical Systems  B, 2006, 6 (1) : 185202. doi: 10.3934/dcdsb.2006.6.185 
[2] 
Timothy C. Reluga, Jan Medlock, Alison Galvani. The discounted reproductive number for epidemiology. Mathematical Biosciences & Engineering, 2009, 6 (2) : 377393. doi: 10.3934/mbe.2009.6.377 
[3] 
S.M. Moghadas. Modelling the effect of imperfect vaccines on disease epidemiology. Discrete & Continuous Dynamical Systems  B, 2004, 4 (4) : 9991012. doi: 10.3934/dcdsb.2004.4.999 
[4] 
W.R. Derrick, P. van den Driessche. Homoclinic orbits in a disease transmission model with nonlinear incidence and nonconstant population. Discrete & Continuous Dynamical Systems  B, 2003, 3 (2) : 299309. doi: 10.3934/dcdsb.2003.3.299 
[5] 
Wenzhang Huang, Maoan Han, Kaiyu Liu. Dynamics of an SIS reactiondiffusion epidemic model for disease transmission. Mathematical Biosciences & Engineering, 2010, 7 (1) : 5166. doi: 10.3934/mbe.2010.7.51 
[6] 
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 
[7] 
Burcu Adivar, Ebru Selin Selen. Compartmental disease transmission models for smallpox. Conference Publications, 2011, 2011 (Special) : 1321. doi: 10.3934/proc.2011.2011.13 
[8] 
Ping Yan. A frailty model for intervention effectiveness against disease transmission when implemented with unobservable heterogeneity. Mathematical Biosciences & Engineering, 2018, 15 (1) : 275298. doi: 10.3934/mbe.2018012 
[9] 
Xia Wang, Yuming Chen. An agestructured vectorborne disease model with horizontal transmission in the host. Mathematical Biosciences & Engineering, 2018, 15 (5) : 10991116. doi: 10.3934/mbe.2018049 
[10] 
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 
[11] 
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 
[12] 
Wandi Ding. Optimal control on hybrid ODE Systems with application to a tick disease model. Mathematical Biosciences & Engineering, 2007, 4 (4) : 633659. doi: 10.3934/mbe.2007.4.633 
[13] 
Mingtao Li, Guiquan Sun, Juan Zhang, Zhen Jin, Xiangdong Sun, Youming Wang, Baoxu Huang, Yaohui Zheng. Transmission dynamics and control for a brucellosis model in Hinggan League of Inner Mongolia, China. Mathematical Biosciences & Engineering, 2014, 11 (5) : 11151137. doi: 10.3934/mbe.2014.11.1115 
[14] 
Yves Dumont, Frederic Chiroleu. Vector control for the Chikungunya disease. Mathematical Biosciences & Engineering, 2010, 7 (2) : 313345. doi: 10.3934/mbe.2010.7.313 
[15] 
Olga Vasilyeva, Tamer Oraby, Frithjof Lutscher. Aggregation and environmental transmission in chronic wasting disease. Mathematical Biosciences & Engineering, 2015, 12 (1) : 209231. doi: 10.3934/mbe.2015.12.209 
[16] 
JingJing Xiang, Juan Wang, LiMing Cai. Global stability of the dengue disease transmission models. Discrete & Continuous Dynamical Systems  B, 2015, 20 (7) : 22172232. doi: 10.3934/dcdsb.2015.20.2217 
[17] 
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 
[18] 
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 
[19] 
Gerardo Chowell, Catherine E. Ammon, Nicolas W. Hengartner, James M. Hyman. Estimating the reproduction number from the initial phase of the Spanish flu pandemic waves in Geneva, Switzerland. Mathematical Biosciences & Engineering, 2007, 4 (3) : 457470. doi: 10.3934/mbe.2007.4.457 
[20] 
Julien Arino, K.L. Cooke, P. van den Driessche, J. VelascoHernández. An epidemiology model that includes a leaky vaccine with a general waning function. Discrete & Continuous Dynamical Systems  B, 2004, 4 (2) : 479495. doi: 10.3934/dcdsb.2004.4.479 
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