# American Institute of Mathematical Sciences

2011, 2011(Special): 467-474. doi: 10.3934/proc.2011.2011.467

## Do longer delays matter? The effect of prolonging delay in CTL activation

 1 Department of Mathematics, Loyola Marymount University, Los Angeles, CA, United States 2 Department of Mathematics, Pomona College, 610 N. College Ave., Claremont, CA 91711

Received  July 2010 Revised  April 2011 Published  October 2011

The activation of a speci c immune response takes place in the lymphoid organs such as the spleen. We present here a simpli ed model of the proliferation of speci c immune cells in the form of a single delay equation. We show that the system can undergo switches in stability as the delay is increased, and we interpret these results in the context of sustaining an e ective immune response to a dendritic cell vaccine.
Citation: Angela Gallegos, Ami Radunskaya. Do longer delays matter? The effect of prolonging delay in CTL activation. Conference Publications, 2011, 2011 (Special) : 467-474. doi: 10.3934/proc.2011.2011.467
 [1] Eugen Stumpf. Local stability analysis of differential equations with state-dependent delay. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 3445-3461. doi: 10.3934/dcds.2016.36.3445 [2] Evelyn Buckwar, Girolama Notarangelo. A note on the analysis of asymptotic mean-square stability properties for systems of linear stochastic delay differential equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (6) : 1521-1531. doi: 10.3934/dcdsb.2013.18.1521 [3] Abdelhai Elazzouzi, Aziz Ouhinou. Optimal regularity and stability analysis in the $\alpha-$Norm for a class of partial functional differential equations with infinite delay. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 115-135. doi: 10.3934/dcds.2011.30.115 [4] Yanqiang Chang, Huabin Chen. Stability analysis of stochastic delay differential equations with Markovian switching driven by Lévy noise. Discrete and Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021301 [5] Jan Sieber, Matthias Wolfrum, Mark Lichtner, Serhiy Yanchuk. On the stability of periodic orbits in delay equations with large delay. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 3109-3134. doi: 10.3934/dcds.2013.33.3109 [6] Luis Barreira, Claudia Valls. Delay equations and nonuniform exponential stability. Discrete and Continuous Dynamical Systems - S, 2008, 1 (2) : 219-223. doi: 10.3934/dcdss.2008.1.219 [7] Tomás Caraballo, Leonid Shaikhet. Stability of delay evolution equations with stochastic perturbations. Communications on Pure and Applied Analysis, 2014, 13 (5) : 2095-2113. doi: 10.3934/cpaa.2014.13.2095 [8] Leonid Berezansky, Elena Braverman. Stability of linear differential equations with a distributed delay. Communications on Pure and Applied Analysis, 2011, 10 (5) : 1361-1375. doi: 10.3934/cpaa.2011.10.1361 [9] Jan Čermák, Jana Hrabalová. Delay-dependent stability criteria for neutral delay differential and difference equations. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4577-4588. doi: 10.3934/dcds.2014.34.4577 [10] Elena Braverman, Sergey Zhukovskiy. Absolute and delay-dependent stability of equations with a distributed delay. Discrete and Continuous Dynamical Systems, 2012, 32 (6) : 2041-2061. doi: 10.3934/dcds.2012.32.2041 [11] Rui Hu, Yuan Yuan. Stability, bifurcation analysis in a neural network model with delay and diffusion. Conference Publications, 2009, 2009 (Special) : 367-376. doi: 10.3934/proc.2009.2009.367 [12] Songbai Guo, Jing-An Cui, Wanbiao Ma. An analysis approach to permanence of a delay differential equations model of microorganism flocculation. Discrete and Continuous Dynamical Systems - B, 2022, 27 (7) : 3831-3844. doi: 10.3934/dcdsb.2021208 [13] Qiang Li, Mei Wei. Existence and asymptotic stability of periodic solutions for neutral evolution equations with delay. Evolution Equations and Control Theory, 2020, 9 (3) : 753-772. doi: 10.3934/eect.2020032 [14] Tomás Caraballo, José Real, T. Taniguchi. The exponential stability of neutral stochastic delay partial differential equations. Discrete and Continuous Dynamical Systems, 2007, 18 (2&3) : 295-313. doi: 10.3934/dcds.2007.18.295 [15] Samuel Bernard, Fabien Crauste. Optimal linear stability condition for scalar differential equations with distributed delay. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 1855-1876. doi: 10.3934/dcdsb.2015.20.1855 [16] Cemil Tunç. Stability, boundedness and uniform boundedness of solutions of nonlinear delay differential equations. Conference Publications, 2011, 2011 (Special) : 1395-1403. doi: 10.3934/proc.2011.2011.1395 [17] Anatoli F. Ivanov, Musa A. Mammadov. Global asymptotic stability in a class of nonlinear differential delay equations. Conference Publications, 2011, 2011 (Special) : 727-736. doi: 10.3934/proc.2011.2011.727 [18] Samuel Bernard, Jacques Bélair, Michael C Mackey. Sufficient conditions for stability of linear differential equations with distributed delay. Discrete and Continuous Dynamical Systems - B, 2001, 1 (2) : 233-256. doi: 10.3934/dcdsb.2001.1.233 [19] Gang Huang, Yasuhiro Takeuchi, Rinko Miyazaki. Stability conditions for a class of delay differential equations in single species population dynamics. Discrete and Continuous Dynamical Systems - B, 2012, 17 (7) : 2451-2464. doi: 10.3934/dcdsb.2012.17.2451 [20] Stéphane Junca, Bruno Lombard. Stability of neutral delay differential equations modeling wave propagation in cracked media. Conference Publications, 2015, 2015 (special) : 678-685. doi: 10.3934/proc.2015.0678

Impact Factor: