The differential equation model of pathogenesis of Kawasaki disease with theoretical analysis

Rong Qiang; Wanbiao Ma; Ke Guo; Hongwu Du; Rong Qiang; Wanbiao Ma; Ke Guo; Hongwu Du

doi:10.3934/mbe.2019175

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 5: 3488-3511. doi: 10.3934/mbe.2019175

Previous Article Next Article

Special Issues

The differential equation model of pathogenesis of Kawasaki disease with theoretical analysis

1.
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing100083, P.R. China
2.
Beijing Key Laboratory for Magneto-Photoelectrical Composite and Interface Science, Universityof Science and Technology Beijing, Beijing 100083, P.R. China
3.
School of Chemistry and Bioengineering, University of Science and Technology Beijing, Beijing100083, P.R. China

Received: 29 January 2019 Accepted: 08 April 2019 Published: 19 April 2019

Fever is a extremely common symptom in infants and young children. Due to the lowresistance of infants and young, long-term fever may cause damage to the child’s body. Clinically,some children with long-term fever was eventually diagnosed with Kawasaki disease (KD). KD, anautoimmune disease, is a systemic vasculitis mainly affecting children younger than 5 years old. Dueto the delayed therapy and diagnosis, coronary artery abnormalities (CAAs) develop in children with KD, and leads to a high risk of acquired heart disease. Later, patients may have myocardial infarctionor even die a sudden death. Unfortunately, at present, the pathogenesis of KD remains unknownand KD lacks of specific and sensitive biomarkers, thus bringing difficulties to diagnosis and therapy.Therefore it is a highly focused topic to research on the mechanism of KD. Some scholars believethat KD is caused by the cross reaction of external infection and organ tissue composition, herebytriggering disorder of the immune system and producing a variety of cytokines. On the basis ofconsidering the cytokines such as vascular endothelial cells, inflammatory factors, adhesion factorsand chemokines, endothelial cell growth factors, put forward a kind of dynamic model of pathogenesisof KD by the theory of ordinary differential equation. It is found that the dynamic model can showcomplex dynamic behavior, such as the forward and backward bifurcation of the equilibria. This articlereveals the possible complexity of KD infection, and provides a theoretical references for the researchof pathogenic mechanism and clinical treatment of KD.
- Kawasaki disease (KD),
- systemic vasculitis,
- differential equation model,
- backward bifurcation,
- stability
Citation: Rong Qiang, Wanbiao Ma, Ke Guo, Hongwu Du. The differential equation model of pathogenesis of Kawasaki disease with theoretical analysis[J]. Mathematical Biosciences and Engineering, 2019, 16(5): 3488-3511. doi: 10.3934/mbe.2019175

Related Papers:

Abstract

Fever is a extremely common symptom in infants and young children. Due to the lowresistance of infants and young, long-term fever may cause damage to the child’s body. Clinically,some children with long-term fever was eventually diagnosed with Kawasaki disease (KD). KD, anautoimmune disease, is a systemic vasculitis mainly affecting children younger than 5 years old. Dueto the delayed therapy and diagnosis, coronary artery abnormalities (CAAs) develop in children with KD, and leads to a high risk of acquired heart disease. Later, patients may have myocardial infarctionor even die a sudden death. Unfortunately, at present, the pathogenesis of KD remains unknownand KD lacks of specific and sensitive biomarkers, thus bringing difficulties to diagnosis and therapy.Therefore it is a highly focused topic to research on the mechanism of KD. Some scholars believethat KD is caused by the cross reaction of external infection and organ tissue composition, herebytriggering disorder of the immune system and producing a variety of cytokines. On the basis ofconsidering the cytokines such as vascular endothelial cells, inflammatory factors, adhesion factorsand chemokines, endothelial cell growth factors, put forward a kind of dynamic model of pathogenesisof KD by the theory of ordinary differential equation. It is found that the dynamic model can showcomplex dynamic behavior, such as the forward and backward bifurcation of the equilibria. This articlereveals the possible complexity of KD infection, and provides a theoretical references for the researchof pathogenic mechanism and clinical treatment of KD.

References

[1]	C. Shao and S. Zhu, Clinical disease and immunity, Science Press, Beijing, 2002.
[2]	T. Kawasaki, Acute febrile mucocutaneous syndrome with lymphoid involvement with specificdesquamation of the fingers and toes in children, Arerugi, 16 (1967), 178–222.
[3]	S. Bayers, S. T. Shulman and A. S. Paller, Kawasaki disease: Part I. Diagnosis, clinical features,and pathogenesis, J. Am. Acad. Dermatol., 69 (2013), 501e1–501e11.
[4]	R. Uehara and E. D. Belay, Epidemiology of Kawasaki Disease in Asia, Europe, and the UnitedStates, J. Epidemiol., 22 (2012), 79–85.
[5]	H. Lue, L. Chen, M. Lin, et al., Epidemiological features of Kawasaki disease in Taiwan, 1976–2007: results of five nationwide questionnaire hospital surveys, Pediatr. Neonatol., 55 (2014),92–96.
[6]	C. Wei, J. Tsai, C. Lin, et al., Increased risk of idiopathic nephrotic syndrome in children withatopic dermatitis, Pediatr. Nephrol., 29 (2014), 2157–2163.
[7]	A. Kentsis, A. Shulman, S. Ahmed, et al., Urine proteomics for discovery of improved diagnosticmarkers of Kawasaki disease, EMBO Mol. Med., 22 (2012), 210–220.
[8]	M. Ayusawa, T. Sonobe, S. Uemura, et al., Revision of diagnostic guidelines for Kawasaki disease(the 5th revised edition), Pediatr. Int, 47 (2005), 232–234.
[9]	C. Galeotti, S. V. Kaveri, R. Cimaz, et al., Predisposing factors, pathogenesis and therapeuticintervention of Kawasaki disease, Drug. Discov. Today, 21 (2016), 1850–1857.
[10]	M. Terai and S. T. Shulman, Prevalence of coronary artery abnormalities in Kawasaki diseaseis highly dependent on gamma globulin dose but independent of salicylate dose, J. Pediatr., 131(1997), 888–893.
[11]	G. B. Kim, J. J. Yu, K. L. Yoon, et al., Medium- or higher-dose acetylsalicylic acid for acuteKawasaki disease and patient outcomes, J. Pediatr., 184 (2016), 125–129.e1.
[12]	J. C. Burns, B. M. Best, A. Mejias, et al., Infliximab treatment of intravenous immunoglobulin-resistant Kawasaki disease, J. Pediatr., 153 (2008), 833–838.
[13]	T. Yang, M. Lin, C. Lu, et al., The prevention of coronary arterial abnormalities in Kawasakidisease: A meta-analysis of the corticosteroid effectiveness, J. Microbiol. Immunol. Infect., 51(2018), 321–331.
[14]	J. Shen, L. Liang and C. Wang, Perifosine inhibits lipopolysaccharide (LPS)-induced tumornecrosis factor (TNF)- production via regulation multiple signaling pathways: new implicationfor Kawasaki disease (KD) treatment, Biochem. Biophys. Res. Commun., 437 (2013), 250–255.
[15]	F. Bajolle, J. F. Meritet, F. Rozenberg, et al., Markers of a recent bocavirus infection in childrenwith Kawasaki disease: a year prospective study, Pathol. Biol., 62 (2014), 365–368.
[16]	L. Chang, C. Lu, P. Shao, et al., Viral infections associated with Kawasaki disease, J. Formos.Med. Assoc., 113 (2014), 148–154.
[17]	N. Principi, D. Rigante and S. Esposito, The role of infection in Kawasaki syndrome, J. Infect.,67 (2013), 1–10.
[18]	A. Harnden, B. Alves and A. Sheikh, Rising incidence of Kawasaki disease in England: analysisof hospital admission data, Bmj, 324 (2002), 1424–1425.
[19]	H. Murata, Experimental candida-induced arteritis in mice. Relation to arteritis in themucocutaneous lymph node syndrome, Microbiol. Immunol., 23 (1979), 825–831.
[20]	A.H.Rowley, S.M.Wolinsky, D.A.Relman, etal., Searchforhighlyconservedviralandbacterialnucleic acid sequences corresponding to an etiologic agent of Kawasaki disease, Pediatr. Res., 36(1994), 567–571.
[21]	R. S. M. Yeung, The etiology of Kawasaki disease: a superantigen-mediated process, Progress Pediatr. Cardiol., 19 (2004), 115–122.
[22]	C. Lin, C. Lin, B. Hwang, et al., Serial changes of serum interleukin-6, interleukin-8, and tumornecrosis factor alpha among patients with Kawasaki disease,J. Pediatr, 121 (1992), 924–926.
[23]	M. Xiao, L. Men, M. Xu, et al., Berberine protects endothelial progenitor cell from damage ofTNF- via the PI3K/AKT/eNOS signaling pathway, J. Pediatr., 743 (2014), 11–16.
[24]	J. S. Hui-Yuen, T. T. Duong and R. S. Yeung, TNF- is necessary for induction of coronary arteryinflammation and aneurysm formation in an animal model of Kawasaki disease, J. Immunol., 176(2006), 6294–6301.
[25]	R. Fukazawa, Y. Uchikoba, Y. Kuramochi, et al., Leukocyte adhesion factor Mac-1 and migrationinhibitory factor-related protein (MRP) on granulocyte plays the essential role for causingvasculitis in kawasaki disease and the gamma globulin therapy inhibit leukocyte-endothelial celladhesion, JACC, 39 (2002), 409.
[26]	M. Terai, K. Yasukawa, S. Narumoto, et al., Vascular endothelial growth factor in acute Kawasakidisease, J. Pediatr., 83 (1999), 337–339.
[27]	S. T. Shulman and A. H. Rowley, Etiology and pathogenesis of Kawasaki disease, Progress Pediatr. Cardiol., 6 (1997), 187–192.
[28]	Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, AcademicPress, Boston, 1993.
[29]	L. Chen, X. Meng and J. Jiao, Biodynamics, Science Press, Beijing, 2009.30. Z. Ma, Y. Zhou and W. Wang, et al., Mathematical Modeling and Research of Epidemic Dynamics,Science Press, Beijing, 2004.
[30]	31. M. A. Nowak and C. R. M. Bangham, Population dynamics of immune responses to persistentvirus, Science, 272 (1996), 74–79.
[31]	32. A. S. Perelson, A. U. Neumann, M. Markowitz, et al., HIV-1 dynamics in vivo: virion clearancerate, infected cell life-span, and viral generation time, Science, 271 (1996), 1582–1586.
[32]	33. D. E. Kirschner and G. F. Webb, A model for the treatment strategy in the chemotherapy of AIDS,Bull. Math. Biol., 58 (1996), 367–390.
[33]	34. A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo, SIAM Rev.,41 (1999), 3–44.
[34]	35. R. Culshaw and S. Ruan, A delay-differential equation model of HIV infection of CD4 + T-cells,Math. Biosci., 165 (2000), 27–39.
[35]	36. M. A. Nowak and R. M. May, Virus Dynamics: Mathematical Principles of Immunology and Virology, Oxford University Press, Oxford, 2000.
[36]	37. Y. Iwasa, F. Michor and M. A. Nowak, Some basic properties of immune selection, J. Theor. Biol.,229 (2004), 179–188.
[37]	38. R. Kumar, G. Clermont, Y. Vodovotz, et al., The dynamics of acute inflammation, J. Theor. Biol.,230 (2004), 145–155.
[38]	39. Y. Xiao, S. Tang and J. Wu, Media impact switching surface during an infectious disease outbreak,Sci. Rep., 5 (2015), 78
[39]	40. S. K. Sasmal, Y. Dong and Y. Takeuchi, Mathematical modeling on T-cell me diate d adaptiveimmunity in primary dengue infections, J. Theor. Biol., 429 (2017), 229–240.
[40]	41. J. K. Hale and S. M. V. Lunel, Introduction to Functional Differential Equations, Springer Verlag,New York, 1993.
[41]	42. O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation ofthe basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365–382.
[42]	43. P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemicequilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48.

Reader Comments

Your name:*

Email:*
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)