참고문헌
- Adamu, M. Y. and Ogenyi, P. (2017), "Parameterized homotopy perturbation method", Nonlinear Sci. Lett. A, 8(2), 240-243.
- Adimy, M., Crauste, F. and Ruan, S. (2005a), "A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia", SIAM J. Appl. Math., 65(4), 1328-1352. https://doi.org/10.1137/040604698.
- Adimy, M., Crauste, F. and Ruan, S. (2005b), "Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics", Nonlinear Anal. Real World Appl., 6(4), 651-670. https://doi.org/10.1016/j.nonrwa.2004.12.010.
- An der Heiden, U. and Mackey, M.C. (1982), "The dynamics of production and destruction: analytic insight into complex behavior", J. Math. Biol., 16(1), 75-101. https://doi.org/10.1007/BF00275162.
- Angelucci, E., Matthes-Martin, S., Baronciani, D., Bernaudin, F., Bonanomi, S., Cappellini, M.D., Dalle, J.H., Di Bartolomeo, P., de Heredia, C.D., Dickerhoff, R., Giardini, C., Gluckman, E., Hussein, A.A., Kamani, N., Minkov, M., Locatelli, F., Rocha, V., Sedlacek, P., Smiers, F., Thuret, F., Yaniv, I., Cavazzana, M. and Peters, C. (2014). "Hematopoietic stem cell transplantation in thalassemia major and sickle cell disease: indications and management recommendations from an international expert panel", Haematologica, 99(5), 811-820. https://doi.org/10.3324/haematol.2013.099747.
- Banerjee, U., Girard, J.R., Goins, L.M. and Spratford, C.M. (2019), "Drosophila as a genetic model for hematopoiesis", Genetics, 211(2), 367-417. https://doi.org/10.1534/genetics.118.300223.
- Belair, J., Mackey, M.C. and Mahaffy, J.M. (1995), "Age-structured and two-delay models for erythropoiesis", Math. Biosci., 128(1-2), 317-346. https://doi.org/10.1016/0025-5564(94)00078-E.
- Crauste, F. (2014), "Equations a retard et modeles de dynamiques de populations cellulaires", Ph.D. Dissertation, Universite Claude Bernard Lyon 1, Lyon.
- Cullen, S.M., Mayle, A., Rossi, L. and Goodell, M.A. (2014), "Hematopoietic stem cell development: an epigenetic journey", Curr. Top. Dev. Biol., 107, 39-75. https://doi.org/10.1016/B978-0-12-416022-4.00002-0.
- Cveticanin, L. (2006), "Homotopy-perturbation method for pure nonlinear differential equation", Chaos Solitons Fractals, 30(5), 1221-1230. https://doi.org/10.1016/J.CHAOS.2005.08.180.
- Dehghan, M. and Shakeri, F. (2007), "Solution of a partial differential equation subject to temperature overspecification by He's homotopy perturbation method", Phys. Scr., 75(6), 778. https://doi.org/10.1088/0031-8949/75/6/007.
- Dehghan, M. and Shakeri, F. (2008a), "Solution of an integro-differential equation arising in oscillating magnetic fields using He's homotopy perturbation method", Electromagn Waves (Camb), 78, 361-376. https://doi.org/10.2528/PIER07090403.
- Dehghan, M. and Shakeri, F. (2008b), "Use of He's homotopy perturbation method for solving a partial differential equation arising in modeling of flow in porous media", J. Porous Media, 11(8) 765-778. https://doi.org/10.1615/JPorMedia.v11.i8.50.
- El-Dib, Y.O. (2017), "Multiple scales homotopy perturbation method for nonlinear oscillators", Nonlinear Sci. Lett. A, 8(4), 352-364.
- Ganji, D.D. and Rafei, M. (2006), "Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method", Phys. Lett. A, 356(2), 131-137. https://doi.org/10.1016/J.PHYSLETA.2006.03.039.
- Ganji, D.D. and Sadighi, A. (2006), "Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations", Int. J. Nonlinear Sci. Numer. Simul., 7(4), 411-418. https://doi.org/10.1515/IJNSNS.2006.7.4.411.
- Ganji, D.D. and Sadighi, A. (2007), "Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations", J. Comput. Appl. Math., 207(1), 24-34. https://doi.org/10.1016/J.CAM.2006.07.030.
- He, J.H. (1999), "Homotopy perturbation technique", Comput. Methods Appl. Mech. Eng., 178(3), 257-262. https://doi.org/10.1016/S0045-7825(99)00018-3.
- He, J.H. (2005), "Application of homotopy perturbation method to nonlinear wave equations", Chaos Solitons Fractals, 26(3), 695-700. https://doi.org/10.1016/J.CHAOS.2005.03.006.
- He, J.H. (2006), "Addendum: new interpretation of homotopy perturbation method", Int. J. Mod. Phys. B, 20(18), 2561-2568. https://doi.org/10.1142/S0217979206034819.
- He, J.H. (2014), "Homotopy perturbation method with two expanding parameters", Indian J. Phys., 88(2), 193-196. https://doi.org/10.1007/s12648-013-0378-1.
- He, J.H. (2012a), "Asymptotic methods for solitary solutions and compactons", Abstr. Appl. Anal., 2012, 916793. https://doi.org/10.1155/2012/916793.
- He, J.H. (2012b), "Homotopy perturbation method with an auxiliary term", Abstr. Appl. Anal, 2012, 857612. https://doi.org/10.1155/2012/857612.
- Kumar, A., D'Souza, S.S. and Thakur, A.S. (2019), "Understanding the journey of human hematopoietic stem cell development", Stem Cells Int., 2019, 2141475. https://doi.org/10.1155/2019/2141475.
- Laurenti, E. and Gottgens, B. (2018), "From haematopoietic stem cells to complex differentiation landscapes", Nature, 553(7689), 418-426. https://doi.org/10.1038/nature25022.
- Mackey, M.C. (1978), "Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis", Blood, 51(5), 941-956. https://doi.org/10.1182/blood.v51.5.941.941
- Mikkola, H.K.A. and Orkin, S.H. (2006), "The journey of developing hematopoietic stem cells", Development, 133(19), 3733-3744. https://doi.org/10.1242/dev.02568.
- Nooney, G.C. (1967), "Age distributions in dividing populations", Biophys. J., 7(1), 69-76. https://doi.org/10.1016/S0006-3495(67)86575-5
- Notta, F., Zandi, S., Takayama, N., Dobson, S., Gan, O.I., Wilson, G., Kaufmann, K.B., McLeod, J., Laurenti, E. and Dunant, C.F. (2016), "Distinct routes of lineage development reshape the human blood hierarchy across ontogeny", Science, 351(6269), aab2116. https://doi.org/10.1126/science.aab2116.
- Pujo-Menjouet, L. and Mackey, M.C. (2004), "Contribution to the study of periodic chronic myelogenous leukemia", C. R. Biol., 327(3), 235-244. https://doi.org/10.1016/j.crvi.2003.05.004.
- Rafei, M., Ganji, D.D. and Daniali, H. (2007), "Solution of the epidemic model by homotopy perturbation method", Appl. Math. Comput., 187(2), 1056-1062. https://doi.org/10.1016/j.amc.2006.09.019.
- Salem, H.K. and Thiemermann, C. (2010), "Mesenchymal stromal cells: Current understanding and clinical status", Stem Cells, 28(3), 585-596. https://doi.org/10.1002/stem.269.
- Stem cells: Sources, types and uses. (2019), https://www.medicalnewstoday.com/articles/323343.php.
- Tomasetti, C. and Vogelstein, B. (2015), "Variation in cancer risk among tissues can be explained by the number of stem cell divisions", Science, 347(6217), 78-81. https://doi.org/10.1126/science.1260825.
- Varn, F.S., Andrews, E.H. and Cheng, C. (2015), "Systematic analysis of hematopoietic gene expression profiles for prognostic prediction in acute myeloid leukemia", Sci. Rep., 5, 16987. https://doi.org/10.1038/srep16987.
- Wang, Q. (2008), "Homotopy perturbation method for fractional KdV-Burgers equation", Chaos Solitons Fractals, 35(5), 843-850. https://doi.org/10.1016/J.CHAOS.2006.05.074.
- Wu, Y. and He, J.H. (2018), "Homotopy perturbation method for nonlinear oscillators with coordinatedependent mass", Results Phys., 10, 270-271. http://dx.doi.org/10.1016/j.rinp.2018.06.015.