-
Previous Article
Subthreshold coexistence of strains: the impact of vaccination and mutation
- MBE Home
- This Issue
-
Next Article
A mathematical model for M-phase specific chemotherapy including the $G_0$-phase and immunoresponse
The role of delays in innate and adaptive immunity to intracellular bacterial infection
1. | Dept. of Microbiology and Immunology, University of Michigan Medical School, 6730 Med. Sci. Bldg. II, Ann Arbor, MI 48109-0620, United States |
2. | Institute of Biomathematics, University of Urbino, Italy |
3. | Dept. of Microbiology and Immunology, University of Michigan Medical School, 6730 Med. Sci. Bldg. II, Ann Arbor, MI 48109-062, United States |
[1] |
H.Thomas Banks, Danielle Robbins, Karyn L. Sutton. Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1301-1333. doi: 10.3934/mbe.2013.10.1301 |
[2] |
Chunhua Shan, Hongjun Gao, Huaiping Zhu. Dynamics of a delay Schistosomiasis model in snail infections. Mathematical Biosciences & Engineering, 2011, 8 (4) : 1099-1115. doi: 10.3934/mbe.2011.8.1099 |
[3] |
Mudassar Imran, Hal L. Smith. The dynamics of bacterial infection, innate immune response, and antibiotic treatment. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 127-143. doi: 10.3934/dcdsb.2007.8.127 |
[4] |
Robert G. McLeod, John F. Brewster, Abba B. Gumel, Dean A. Slonowsky. Sensitivity and uncertainty analyses for a SARS model with time-varying inputs and outputs. Mathematical Biosciences & Engineering, 2006, 3 (3) : 527-544. doi: 10.3934/mbe.2006.3.527 |
[5] |
Eugen Stumpf. Local stability analysis of differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3445-3461. doi: 10.3934/dcds.2016.36.3445 |
[6] |
Qiang Guo, Dong Liang. An adaptive wavelet method and its analysis for parabolic equations. Numerical Algebra, Control & Optimization, 2013, 3 (2) : 327-345. doi: 10.3934/naco.2013.3.327 |
[7] |
Songbai Guo, Wanbiao Ma. Global behavior of delay differential equations model of HIV infection with apoptosis. Discrete & Continuous Dynamical Systems - B, 2016, 21 (1) : 103-119. doi: 10.3934/dcdsb.2016.21.103 |
[8] |
Mugen Huang, Moxun Tang, Jianshe Yu, Bo Zheng. A stage structured model of delay differential equations for Aedes mosquito population suppression. Discrete & Continuous Dynamical Systems - A, 2019, 0 (0) : 0-0. doi: 10.3934/dcds.2020042 |
[9] |
Yuhua Zhu. A local sensitivity and regularity analysis for the Vlasov-Poisson-Fokker-Planck system with multi-dimensional uncertainty and the spectral convergence of the stochastic Galerkin method. Networks & Heterogeneous Media, 2019, 14 (4) : 677-707. doi: 10.3934/nhm.2019027 |
[10] |
Tatiana Filippova. Differential equations of ellipsoidal state estimates in nonlinear control problems under uncertainty. Conference Publications, 2011, 2011 (Special) : 410-419. doi: 10.3934/proc.2011.2011.410 |
[11] |
Sun Yi, Patrick W. Nelson, A. Galip Ulsoy. Delay differential equations via the matrix lambert w function and bifurcation analysis: application to machine tool chatter. Mathematical Biosciences & Engineering, 2007, 4 (2) : 355-368. doi: 10.3934/mbe.2007.4.355 |
[12] |
Evelyn Buckwar, Girolama Notarangelo. A note on the analysis of asymptotic mean-square stability properties for systems of linear stochastic delay differential equations. Discrete & Continuous Dynamical Systems - B, 2013, 18 (6) : 1521-1531. doi: 10.3934/dcdsb.2013.18.1521 |
[13] |
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 & Continuous Dynamical Systems - A, 2011, 30 (1) : 115-135. doi: 10.3934/dcds.2011.30.115 |
[14] |
Hedia Fgaier, Hermann J. Eberl. Parameter identification and quantitative comparison of differential equations that describe physiological adaptation of a bacterial population under iron limitation. Conference Publications, 2009, 2009 (Special) : 230-239. doi: 10.3934/proc.2009.2009.230 |
[15] |
Michael Dellnitz, Mirko Hessel-Von Molo, Adrian Ziessler. On the computation of attractors for delay differential equations. Journal of Computational Dynamics, 2016, 3 (1) : 93-112. doi: 10.3934/jcd.2016005 |
[16] |
Hermann Brunner, Stefano Maset. Time transformations for delay differential equations. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 751-775. doi: 10.3934/dcds.2009.25.751 |
[17] |
Klaudiusz Wójcik, Piotr Zgliczyński. Topological horseshoes and delay differential equations. Discrete & Continuous Dynamical Systems - A, 2005, 12 (5) : 827-852. doi: 10.3934/dcds.2005.12.827 |
[18] |
Seung-Yeal Ha, Shi Jin. Local sensitivity analysis for the Cucker-Smale model with random inputs. Kinetic & Related Models, 2018, 11 (4) : 859-889. doi: 10.3934/krm.2018034 |
[19] |
Jia Li. A malaria model with partial immunity in humans. Mathematical Biosciences & Engineering, 2008, 5 (4) : 789-801. doi: 10.3934/mbe.2008.5.789 |
[20] |
Teresa Faria, José J. Oliveira. On stability for impulsive delay differential equations and application to a periodic Lasota-Wazewska model. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2451-2472. doi: 10.3934/dcdsb.2016055 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]