[1]
|
M. Ayusawa, T. Sonobe, S. Uemura, S. Ogawa, Y. Nakamura, N. Kiyosawa, M. Ishii and K. Harada, Revision of diagnostic guidelines for Kawasaki disease (the 5th revised edition), Pediatr. Int., 47 (2005), 232-234.
doi: 10.1111/j.1442-200x.2005.02033.x.
|
[2]
|
E. j. Benjamin, S. S. Virani, C. W. Callaway, et al., Heart disease and stroke statistics-2018 update: A report from the American Heart Association, Circulation, 137 (2018), e67–e492.
doi: 10.1161/CIR.0000000000000558.
|
[3]
|
M. Cartwright and M. Husain, A model for the control of testosterone secretion, J.Theoret. Biol., 123 (1986), 239-250.
doi: 10.1016/S0022-5193(86)80158-8.
|
[4]
|
R. V. Culshaw and S. Ruan, A delay-differential equation model of HIV infection of CD$4^{+}$ T-cells, Math. Biosci., 165 (2000), 27-39.
doi: 10.1016/S0025-5564(00)00006-7.
|
[5]
|
S. Chen, C. Cheng and Y. Takeuchi, Stability analysis in delayed within-host viral dynamics with both viral and cellular infections, J. Math. Anal. Appl., 442 (2016), 642-672.
doi: 10.1016/j.jmaa.2016.05.003.
|
[6]
|
H. Dahari, A. Lo, R. M. Ribeiro and A. S. Perelson, Modeling hepatitis C virus dynamics: Liver regeneration and critical drug efficacy, J. Theoret. Biol., 247 (2007), 371-381.
doi: 10.1016/j.jtbi.2007.03.006.
|
[7]
|
Y. Enatsu, Y. Nakata and Y. Muroya, Lyapunov functional techniques for the global stability analysis of a delayed SIRS epidemic model, Nonlinear. Anal. Real World Appl., 13 (2012), 2120-2133.
doi: 10.1016/j.nonrwa.2012.01.007.
|
[8]
|
C. Galeotti, S. V. Kaveri, R. Cimaz, I. Koné-Paut and J. Bayry, Predisposing factors, pathogenesis and therapeutic intervention of Kawasaki disease, Drug. Discov. Today., 21 (2016), 1850-1857.
doi: 10.1016/j.drudis.2016.08.004.
|
[9]
|
K. Guo, W. Ma and R. Qiang, On global stability of the equilibria of an ordinary differential equation model of Kawasaki disease pathogenesis, Appl. Math. Lett., 106 (2020), 106319, 10pp.
doi: 10.1016/j.aml.2020.106319.
|
[10]
|
S. Guo and W. Ma, Global behavior of delay differential equations model of HIV infection with apoptosis, Discrete Contin. Dyn. Syst. Ser. B, 21 (2016), 103-119.
doi: 10.3934/dcdsb.2016.21.103.
|
[11]
|
J. K. Hale, Theory of Functional Differential Equations, 2$^{nd}$ edition, Springer-Verlag, New York, 1977.
doi: 10.1007/978-1-4612-9892-2.
|
[12]
|
J. S. Hui-Yuen, T. T. Duong and R. S. Yeung, TNF-$\alpha$ is necessary for induction of coronary artery inflammation and aneurysm formation in an animal model of Kawasaki disease, J. Immunol., 176 (2006), 6294-6301.
doi: 10.4049/jimmunol.176.10.6294.
|
[13]
|
F. Jiao, A. K. Jindal, V. Pandiarajan, R. Khubchandani, N. Kamath, T. Sabui, R. Mondal, P. Pal and S. Singh, The emergence of Kawasaki disease in India and China, Glob. Cardiol. Sci. Pract., 2017 (2017), e201721.
doi: 10.21542/gcsp.2017.21.
|
[14]
|
T. Kawasaki, Acute febrile mucocutaneous syndrome with lymphoid involvement with specific desquamation of the fingers and toes in children, Arerugi, 16 (1967), 178–222 (in Japanese).
|
[15]
|
A. Kentsis, A. Shulman, S. Ahmed and et al., Urine proteomics for discovery of improved diagnostic markers of Kawasaki disease, EMBO Mol. Med., 5 (2013), 210-220.
doi: 10.1002/emmm.201201494.
|
[16]
|
D. Kirschner and J. C. Panetta, Modelling immunotherapy of the tumor-immune interaction, J. Math. Biol., 37 (1998), 235-252.
doi: 10.1007/s002850050127.
|
[17]
|
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, 1993.
|
[18]
|
A. J. Kucharski, S. Funk, R. M. Eggo, H. P. Mallet, W. J. Edmunds and E. J. Nilles, Transmission dynamics of Zika virus in island populations: a modelling analysis of the 2013-14 French Polynesia outbreak, PLoS. Negl. Trop. Dis., 10 (2016), e0004726.
doi: 10.1371/journal.pntd.0004726.
|
[19]
|
K. Kudo, S. Hasegawa, Y. Suzuki, R. Hirano, H. Wakiguchi, S. Kittaka and T. Ichiyama, $1\alpha$, $25$-Dihydroxyvitamin $D_3$ inhibits vascular cellular adhesion molecule-1 expression and interleukin-8 production in human coronary arterial endothelial cells, J. Steroid Biochem. Mol. Biol., 132 (2012), 290-294.
doi: 10.1016/j.jsbmb.2012.07.003.
|
[20]
|
D. Li and W. Ma, Asymptotic properties of a HIV-1 infection model with time delay, J. Math. Anal. Appl., 335 (2007), 683-691.
doi: 10.1016/j.jmaa.2007.02.006.
|
[21]
|
C. Y. Lin, C. C. Lin, B. Hwang and B. Chiang, Serial changes of serum interleukin-6, interleukin-8, and tumor necrosis factor alpha among patients with Kawasaki disease, J. Pediatr., 121 (1992), 924-926.
doi: 10.1016/S0022-3476(05)80343-9.
|
[22]
|
N. Makino, Y. Nakamura, M. Yashiro, R. Ae, S. Tsuboi, Y. Aoyama, T. Kojo, R. Uehara, K. Kotani and H. Yanagawa, Descriptive epidemiology of Kawasaki disease in Japan, 2011-2012: from the results of the 22nd nationwide survey, J. Epidemiol., 25 (2015), 239-245.
doi: 10.2188/jea.JE20140089.
|
[23]
|
B. W. McCrindle, A. H. Rowley, J. W. Newburger, et al., Diagnosis, treatment, and long-term management of Kawasaki disease: a scientific statement for health professionals from the American Heart Association, Circulation, 135 (2017), e927–e999.
doi: 10.1161/CIR.0000000000000484.
|
[24]
|
A. U. Neumann, N. P. Lam, H. Dahari, D. R. Gretch, T. E. Wiley, T. J. Layden and A. S. Perelson, Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-$\alpha$ therapy, Science, 282 (1998), 103-107.
doi: 10.1126/science.282.5386.103.
|
[25]
|
J. W. Newburger, M. Takahashi, M. A. Gerber and et al., Diagnosis, treatment, and long-term management of Kawasaki disease: A statement for health professionals from the Committee on Rheumatic Fever, Endocarditis and Kawasaki Disease, Council on Cardiovascular Disease in the Young, American Heart Association, Circulation, 110 (2004), 2747-2771.
doi: 10.1161/01.CIR.0000145143.19711.78.
|
[26]
|
M. A. Nowak and C. R. M. Bangham, Population dynamics of immune responses to persistent virus, Science, 272 (5258), 74-79.
doi: 10.1126/science.272.5258.74.
|
[27]
|
A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev., 41 (1999), 3-44.
doi: 10.1137/S0036144598335107.
|
[28]
|
R. Qiang, W. Ma, K. Guo and H. Du, The differential equation model of pathogenesis of Kawasaki disease with theoretical analysis, Math. Biosci. Eng., 16 (2019), 3488-3511.
doi: 10.3934/mbe.2019175.
|
[29]
|
C. M. Saad-Roy, J. Ma and P. van den Driessche, The effect of sexual transmission on Zika virus dynamics, J. Math. Biol., 77 (2018), 1917-1941.
doi: 10.1007/s00285-018-1230-1.
|
[30]
|
J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice hall, Englewood Cliffs, 1991.
|
[31]
|
J. Tam, Delay effect in a model for virus replication, IMA J. Math. Appl. Med. Biol., 16 (1999), 29-37.
doi: 10.1093/imammb/16.1.29.
|
[32]
|
M. Terai, K. Yasukawa, S. Narumoto, S. Tateno, S. Oana and Y. Kohno, Vascular endothelial growth factor in acute Kawasaki disease, Am. J. Pediatr., 83 (1999), 337-339.
doi: 10.1016/S0002-9149(98)00864-9.
|
[33]
|
R. Uehara and E. D. Belay, Epidemiology of Kawasaki Disease in Asia, Europe, and the United States, J. Epidemiol., 22 (2012), 79-85.
doi: 10.2188/jea.JE20110131.
|
[34]
|
W. Wang, Global behavior of a SEIRS epidemic model with time delays, Appl. Math. Lett., 15 (2002), 423-428.
doi: 10.1016/S0893-9659(01)00153-7.
|
[35]
|
X. Wang, S. Liu and L. Rong, Permanence and extinction of a non-autonomous HIV-1 model with time delays, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), 1783-1800.
doi: 10.3934/dcdsb.2014.19.1783.
|
[36]
|
M. Xiao, L. Men, M. Xu, G. Wang, H. Lv and C. Liu, Berberine protects endothelial progenitor cell from damage of TNF-$\alpha$ via the PI3K/AKT/eNOS signaling pathway, Eur. J. Pharmacol., 743 (2014), 11-16.
doi: 10.1016/j.ejphar.2014.09.024.
|
[37]
|
R. S. M. Yeung, The etiology of Kawasaki disease: A superantigen-mediated process, Prog. Pediatr. Cardiol., 19 (2004), 115-122.
doi: 10.1016/j.ppedcard.2004.08.004.
|