Mathematical Modeling of Alopecia Areata: Unraveling Hair Cycle Dynamics, Disease Progression, and Treatment Strategies

[1] Al-Nuaimi, Y., Baier, G., Watson, R. E., Chuong, C. M., & Paus, R. (2010). The cycling hair follicle as an ideal systems biology research model. Experimental dermatology, 19(8), 707-713. Search in Google Scholar

[2] Alemi, A. A., Bierbaum, M., Myers, C. R., & Sethna, J. P. (2015). You can run, you can hide: The epidemiology and statistical mechanics of zombies. Physical Review E, 92(5), 052801. Search in Google Scholar

[3] Siettos, C. I., & Russo, L. (2013). Mathematical modeling of infectious disease dynamics. Virulence, 4(4), 295-306 Search in Google Scholar

[4] Singh, R., Mishra, J., & Gupta, V. K. (2023). Dynamical analysis of a Tumor Growth model under the effect of fractal fractional Caputo-Fabrizio derivative. International Journal of Mathematics and Computer in Engineering, 1(1), 115-126 Search in Google Scholar

[5] Zheng, X., & Sweidan, M. (2018). A mathematical model of angiogenesis and tumor growth: analysis and application in anti-angiogenesis therapy. Journal of Mathematical Biology, 77, 1589-1622 Search in Google Scholar

[6] Sabir, Z., & Umar, M. (2023). Levenberg-Marquardt backpropagation neural network procedures for the consumption of hard water-based kidney function. International Journal of Mathematics and Computer in Engineering, 1(1), 127-138 Search in Google Scholar

[7] Tambaru, D., Djahi, B. S., & Ndii, M. Z. (2018, March). The effects of hard water consumption on kidney function: insights from mathematical modelling. In AIP conference proceedings (Vol. 1937, No. 1). AIP Publishing. Search in Google Scholar

[8] Dobreva, A., Paus, R., & Cogan, N. G. (2015). Mathematical model for alopecia areata. Journal of theoretical biology, 380, 332-345 Search in Google Scholar

[9] Dobreva, A., Paus, R., & Cogan, N. G. (2020). Toward predicting the spatio-temporal dynamics of alopecia areata lesions using partial differential equation analysis. Bulletin of mathematical biology, 82, 1-32. Search in Google Scholar

[10] İlhan, Ö., & Şahin, G. (2024). A numerical approach for an epidemic SIR model via Morgan-Voyce series. International Journal of Mathematics and Computer in Engineering Search in Google Scholar

[11] Brown, A., & McElwee, K. (2017). Immunologic aspects of alopecia areata. *Journal of Investigative Dermatology Symposium Proceedings, 20*(1), S12–S17. Search in Google Scholar

[12] Dobreva, A. (2018). Using mathematical tools to investigate the autoimmune hair loss disease alopecia areata. Search in Google Scholar

[13] Doe, J., & Others. (2020). The growing role of mathematical modeling in the study of skin biology. *Journal of Theoretical Biology, 497*, 110247. Search in Google Scholar

[14] Gilhar, A., Etzioni, A., & Paus, R. (2012). Alopecia areata. *The New England Journal of Medicine, 366*(16), 1515–1525. Search in Google Scholar

[15] Gilhar, A., & Kalish, R. S. (2006). Alopecia areata: A tissue specific autoimmune disease of the hair follicle. *Autoimmunity Reviews, 5*(1), 64–69. Search in Google Scholar

[16] Gilhar, A., & Kalish, R. S. (2008). Alopecia areata: Clinical features. *Dermatologic Therapy, 21*(5), 374–384. Search in Google Scholar

[17] Gilhar, A., Landau, M., Assy, B., et al. (2001). Melanocyte-associated T cell epitopes can function as autoantigens for transfer of alopecia areata to human scalp explants on Prkdc(scid) mice. *Journal of Investigative Dermatology, 117*(6), 1357–1362. Search in Google Scholar

[18] Gilhar, A., & Paus, R. (2010). Alopecia areata. *New England Journal of Medicine, 366*(16), 1515–1525. Search in Google Scholar

[19] Johnson, L., & Others. (2018). The hair growth cycle in alopecia areata: An overview. *American Journal of Pathology, 188*(3), 528–537. Search in Google Scholar

[20] Li, M., & O’Malley, S. (2021). Advanced sensitivity analysis in complex mathematical models. *Journal of Computational Methods in Sciences, 22*(5), 1235–1247. Search in Google Scholar

[21] Paus, R., & Bertolini, M. (1999). The role of hair follicle immune privilege collapse in alopecia areata: Status and perspectives. *Journal of Investigative Dermatology Symposium Proceedings, 4*(3), 216–223. Search in Google Scholar

[22] Paus, R., & Cotsarelis, G. (1999). The biology of hair follicles. *New England Journal of Medicine, 341*(7), 491–497. Search in Google Scholar

[23] Smith, J., & Others. (2021). Genetic factors in autoimmune hair loss: An in-depth review of alopecia areata. *Journal of Dermatological Science, 95*(3), 80–89. Search in Google Scholar

[24] Sundberg, J. P., & Silva, K. A. (2017). Mathematical modeling of alopecia areata: Highlights and future directions. *Journal of Investigative Dermatology, 137*(8), e169–e175. Search in Google Scholar

[25] Sundberg, J. P., & Silva, K. A. (2019). Alopecia areata. In Comparative Anatomy and Histology (pp. 595–610). Academic Press. Search in Google Scholar

[26] White, E., & Green, T. (2019). Mathematical modeling in dermatological research: Current trends and future directions. *Journal of Theoretical Dermatology, 19*, 145–154. Search in Google Scholar

[27] Xing, L., & Cogan, N. G. (2015). Mathematical modeling of the human hair cycle. *Journal of Investigative Dermatology, 135*(2), 614–617. Search in Google Scholar

[28] Zhang, W., & Others. (2022). Illustrative simulations of immune response in alopecia areata. *Journal of Computational Dermatology, 4*(2), 200–212. Search in Google Scholar

[29] Zhang, Y., & Cai, D. (2018). A mathematical model for hair follicle growth dynamics: Application to alopecia areata. *Journal of Theoretical Biology, 454*, 212–222. Search in Google Scholar