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A Simple Epidemic Model with Surprising Dynamics
The Effects of Affinity Mediated Clonal Expansion of Premigrant Thymocytes on the Periphery TCell Repertoire
1.  Department of Pathology and laboratory Medicine, The University of Texas Medical School at Houston, Houston, TX 77030 
[1] 
D. Criaco, M. Dolfin, L. Restuccia. Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cells. Mathematical Biosciences & Engineering, 2013, 10 (1) : 5973. doi: 10.3934/mbe.2013.10.59 
[2] 
Lisette dePillis, Trevor Caldwell, Elizabeth Sarapata, Heather Williams. Mathematical modeling of regulatory T cell effects on renal cell carcinoma treatment. Discrete & Continuous Dynamical Systems  B, 2013, 18 (4) : 915943. doi: 10.3934/dcdsb.2013.18.915 
[3] 
Hongjing Shi, Wanbiao Ma. An improved model of t cell development in the thymus and its stability analysis. Mathematical Biosciences & Engineering, 2006, 3 (1) : 237248. doi: 10.3934/mbe.2006.3.237 
[4] 
Yueping Dong, Rinko Miyazaki, Yasuhiro Takeuchi. Mathematical modeling on helper T cells in a tumor immune system. Discrete & Continuous Dynamical Systems  B, 2014, 19 (1) : 5572. doi: 10.3934/dcdsb.2014.19.55 
[5] 
Amy H. Lin Erickson, Alison Wise, Stephen Fleming, Margaret Baird, Zabeen Lateef, Annette Molinaro, Miranda TebohEwungkem, Lisette dePillis. A preliminary mathematical model of skin dendritic cell trafficking and induction of T cell immunity. Discrete & Continuous Dynamical Systems  B, 2009, 12 (2) : 323336. doi: 10.3934/dcdsb.2009.12.323 
[6] 
Reihaneh Mostolizadeh, Zahra Afsharnezhad, Anna MarciniakCzochra. Mathematical model of Chimeric Antigene Receptor (CAR) T cell therapy with presence of cytokine. Numerical Algebra, Control & Optimization, 2018, 8 (1) : 6380. doi: 10.3934/naco.2018004 
[7] 
Houssein Ayoub, Bedreddine Ainseba, Michel Langlais, Rodolphe Thiébaut. Parameters identification for a model of T cell homeostasis. Mathematical Biosciences & Engineering, 2015, 12 (5) : 917936. doi: 10.3934/mbe.2015.12.917 
[8] 
Cliburn Chan, Andrew J.T. George, Jaroslav Stark. T cell sensitivity and specificity  kinetic proofreading revisited. Discrete & Continuous Dynamical Systems  B, 2003, 3 (3) : 343360. doi: 10.3934/dcdsb.2003.3.343 
[9] 
Yinghui Dong, Guojing Wang. Ruin probability for renewal risk model with negative risk sums. Journal of Industrial & Management Optimization, 2006, 2 (2) : 229236. doi: 10.3934/jimo.2006.2.229 
[10] 
Oleg U. Kirnasovsky, Yuri Kogan, Zvia Agur. Resilience in stem cell renewal: development of the AgurDanielGinosar model. Discrete & Continuous Dynamical Systems  B, 2008, 10 (1) : 129148. doi: 10.3934/dcdsb.2008.10.129 
[11] 
Bing Liu, Ming Zhou. Robust portfolio selection for individuals: Minimizing the probability of lifetime ruin. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020005 
[12] 
Avner Friedman, Wenrui Hao. Mathematical modeling of liver fibrosis. Mathematical Biosciences & Engineering, 2017, 14 (1) : 143164. doi: 10.3934/mbe.2017010 
[13] 
Guanyu Wang, Gerhard R. F. Krueger. A General Mathematical Method for Investigating the Thymic Microenvironment, Thymocyte Development, and Immunopathogenesis. Mathematical Biosciences & Engineering, 2004, 1 (2) : 289305. doi: 10.3934/mbe.2004.1.289 
[14] 
Fadoua El Moustaid, Amina Eladdadi, Lafras Uys. Modeling bacterial attachment to surfaces as an early stage of biofilm development. Mathematical Biosciences & Engineering, 2013, 10 (3) : 821842. doi: 10.3934/mbe.2013.10.821 
[15] 
Liancheng Wang, Sean Ellermeyer. HIV infection and CD4+ T cell dynamics. Discrete & Continuous Dynamical Systems  B, 2006, 6 (6) : 14171430. doi: 10.3934/dcdsb.2006.6.1417 
[16] 
YuHsien Chang, GuoChin Jau. The behavior of the solution for a mathematical model for analysis of the cell cycle. Communications on Pure & Applied Analysis, 2006, 5 (4) : 779792. doi: 10.3934/cpaa.2006.5.779 
[17] 
Mostafa Adimy, Oscar Angulo, Catherine Marquet, Leila Sebaa. A mathematical model of multistage hematopoietic cell lineages. Discrete & Continuous Dynamical Systems  B, 2014, 19 (1) : 126. doi: 10.3934/dcdsb.2014.19.1 
[18] 
Gang Bao. Mathematical modeling of nonlinear diffracvtive optics. Conference Publications, 1998, 1998 (Special) : 8999. doi: 10.3934/proc.1998.1998.89 
[19] 
Michael Leguèbe. Cell scale modeling of electropermeabilization by periodic pulses. Mathematical Biosciences & Engineering, 2015, 12 (3) : 537554. doi: 10.3934/mbe.2015.12.537 
[20] 
A. Chauviere, T. Hillen, L. Preziosi. Modeling cell movement in anisotropic and heterogeneous network tissues. Networks & Heterogeneous Media, 2007, 2 (2) : 333357. doi: 10.3934/nhm.2007.2.333 
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