[1]
|
V. D. Alvarez-Jiménez, K. Leyva-Paredes, M. García-Martínez, L. Vázquez-Flores and I. Estrada-García, Extracellular vesicles released from Mycobacterium tuberculosis-infected neutrophils promote macrophage autophagy and decrease intracellular mycobacterial survival, Front. Immunol., 9 (2018), 272.
|
[2]
|
L. Cai, G. Chen and D. Xiao, Multiparametric bifurcations of an epidemiological model with strong Allee effect, J. Math. Biol., 67 (2013), 185-215.
doi: 10.1007/s00285-012-0546-5.
|
[3]
|
C. Castillo-Chavez and B. Song, Dynamical models of tuberculosis and their applications, Math. Biosci. Eng., 1 (2004), 361-404.
doi: 10.3934/mbe.2004.1.361.
|
[4]
|
J. Day, A. Friedman and L. S. Schlesinger, Modeling the immune rheostat of macrophages in the lung in response to infection, Proc. Natl. Acad. Sci. USA, 106 (2009), 11246-11251.
|
[5]
|
Y. Du, J. Wu and J. M. Heffernan, A simple in-host model for Mycobacterium tuberculosis that captures all infection outcomes, Math. Popul. Stud., 24 (2017), 37-63.
doi: 10.1080/08898480.2015.1054220.
|
[6]
|
F. Dumortier, R. Roussarie, J. Sotomayor and H. Żaładek, Bifurcations of Planar Vector Fields, Nilpotent Singularities and Abelian Integrals, Lecture Notes in Mathematics, 1480. Springer-Verlag, Berlin, 1991.
doi: 10.1007/BFb0098353.
|
[7]
|
J. L. Flynn, Immunology of tuberculosis and implications in vaccine development, Tuberculosis, 84 (2004), 93-101.
doi: 10.1016/j.tube.2003.08.010.
|
[8]
|
J. L. Flynn and J. Chan, Immunology of tuberculosis, Annu. Rev. Immunol., 19 (2001), 93-129.
|
[9]
|
D. Gammack, S. Ganguli, S. Marino, J. L. Segoviajuarez and D. E. Kirschner, Understanding the immune response in tuberculosis using different mathematical models and biological scales, Multiscale Model. Simul., 3 (2005), 312-345.
doi: 10.1137/040603127.
|
[10]
|
C. Gong, J. J. Linderman and D. Kirschner, A population model capture dynamics of tuberculosis granulomas predicts host infection outcomes, Math. Biosci. Eng., 12 (2015), 625-642.
doi: 10.3934/mbe.2015.12.625.
|
[11]
|
D. He, Q. Wang and W.-C. Lo, Mathematical analysis of macrophage-bateria interaction in tuberculosis infection, Discrete Contin. Dyn. Syst. Ser. B, 23 (2018), 3387-3413.
doi: 10.3934/dcdsb.2018239.
|
[12]
|
J. M. Heffernan, R. J. Smith and L. M. Wahl, Perspectives on the basic reproductive ratio, J. R. Soc. Interface, 2 (2005), 281-293.
|
[13]
|
E. Ibargüen-Mondragón, L. Esteva and E. M. Burbano-Rosero, Mathematical model for the growth of Mycobacterium tuberculosis in the granuloma, Math. Biosci. Eng., 15 (2017), 407-428.
doi: 10.3934/mbe.2018018.
|
[14]
|
E. Ibarguenmondragon, L. Esteva and L. Chavezgalan, A mathematical model for cellular immunology of tuberculosis, Math. Biosci. Eng., 8 (2011), 973-986.
doi: 10.3934/mbe.2011.8.973.
|
[15]
|
A. Kahnert, P. Seiler, M. Stein, S. Bandermann, K. Hahnke, H. J. Mollenkopf and S. H. E. Kaufmann, Alternative activation deprives macrophages of a coordinated defense program to Mycobacterium tuberculosis, Eur. J. Immunol., 36 (2006), 631-647.
|
[16]
|
P. L. Lin and J. L. Flynn, Understanding latent tuberculosis: A moving target, J. Immunol., 185 (2010), 15-22.
doi: 10.4049/jimmunol.0903856.
|
[17]
|
S. Marino and D. E. Kirschner, The human immune response to Mycobacterium tuberculosis in lung and lymph node, J. Theoret. Biol., 227 (2004), 463-486.
doi: 10.1016/j.jtbi.2003.11.023.
|
[18]
|
L. Ramakrishnan, Revisiting the role of the granuloma in tuberculosis, Nat. Rev. Immunol., 12 (2012), 352-366.
doi: 10.1038/nri3211.
|
[19]
|
N. V. Serbina and J. L. Flynn, Early emergence of CD8$^+$ T cells primed for production of type 1 cytokines in the lungs of Mycobacterium tuberculosis-infected mice, Infect. Immun., 67 (1999), 3980-3988.
doi: 10.1128/IAI.67.8.3980-3988.1999.
|
[20]
|
N. V. Serbina, C. C. Liu, C. A. Scanga and J. L. Flynn, CD8$^+$ CTL from lungs of Mycobacterium tuberculosis-infected mice express perforin in vivo and Lyse infected macrophages, J. Immunol., 165 (2000), 353-363.
doi: 10.4049/jimmunol.165.1.353.
|
[21]
|
C. Shan, Y. Yi and H. Zhu, Nilpotent singularities and dynamics in an SIR type of compartmental model with hospital resources, J. Differential Equations, 260 (2016), 4339-4365.
doi: 10.1016/j.jde.2015.11.009.
|
[22]
|
R. Shi, Y. Li and S. Tang, A mathematical model with optimal control for cellular immunology of tuberculosis, Taiwanese J. Math., 18 (2014), 575-597.
doi: 10.11650/tjm.18.2014.3739.
|
[23]
|
D. Sud, C. Bigbee, J. L. Flynn and D. E. Kirschner, Contribution of CD8$^+$ T cells to control of Mycobacterium tuberculosis infection, J. Immunol., 176 (2006), 4296-4314.
doi: 10.4049/jimmunol.177.8.5747-a.
|
[24]
|
M. Travar, M. Petkovic and A. Verhaz, Type â…, â…¡, and â…¢ interferons: Regulating immunity to Mycobacterium tuberculosis infection, Arch. Immunol. Ther. Ex., 64 (2016), 19-31.
doi: 10.1007/s00005-015-0365-7.
|
[25]
|
J. E. Wigginton and D. Kirschner, A model to predict cell-mediated immune regulatory mechanisms during human infection with Mycobacterium tuberculosis, J. Immunol., 166 (2001), 1951-1967.
|
[26]
|
World Health Organization, Global tuberculosis report 2016, (2016), https://www.who.int/tb/publications/2016/en/.
|
[27]
|
World Health Organization, Global tuberculosis report 2019, (2019), https://www.who.int/tb/publications/global_report/en/.
|
[28]
|
P. Yu, Closed-form conditions of bifurcation points for general differential equations, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 15 (2005), 1467-1483.
doi: 10.1142/S0218127405012582.
|
[29]
|
W. Zhang, Analysis of an in-host tuberculosis model for disease control, Appl. Math. Lett., 99 (2020), 105983, 7 pp.
doi: 10.1016/j.aml.2019.07.014.
|