Citation: Frédérique Clément, Béatrice Laroche, Frédérique Robin. Analysis and numerical simulation of an inverse problem for a structured cell population dynamics model[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 3018-3046. doi: 10.3934/mbe.2019150
[1] | M. E. Gurtin and R. C. MacCamy, Non-linear age-dependent population dynamics, Arch. Ration. Mech. Anal., 54(1974): 281–300. |
[2] | B. L. Keyfitz and N. Keyfitz, The McKendrick partial differential equation and its uses in epidemiology and population study, Math. Comput. Model., 26(1997): 1–9. |
[3] | L. M. Abia, O. Angulo and J. C. López-Marcos, Age-structured population models and their numerical solution, Ecol. Modell., 188(2005):112–136. |
[4] | C. Chiu, Nonlinear age-dependent models for prediction of population growth, Math. Biosci., 99(1990): 119–133. |
[5] | A. M. de Roos, Numerical methods for structured population models: the escalator boxcar train, Numer. Methods Partial. Differ. Equ., 4(1988): 173–195. |
[6] | W. Rundell, Determining the birth function for an age structured population, Math. Popul. Stud., 1(1989): 377–395. |
[7] | W. Rundell, Determining the death rate for an age-structured population from census data, SIAM J. Appl. Math., 53(1993): 1731–1746. |
[8] | M. Gyllenberg, A. Osipov, and L. Pivrinta, The inverse problem of linear age-structured population dynamics, J. Evol. Equ., 2(2002): 223–239. |
[9] | A. J. Lotka, The structure of a growing population, Hum. Biol., 3(1931): 459–493. |
[10] | A. J. Lotka, On an integral equation in population analysis, Ann. Math. Stat., 10(1939): 144–161. |
[11] | F. Clément, F. Robin and R. Yvinec, Analysis and calibration of a linear model for structured cell populations with unidirectional motion : Application to the morphogenesis of ovarian follicles, SIAM J. Appl. Math., 79(2019): 207–229. |
[12] | P. Gabriel, Measure solutions to the conservative renewal equation. ESAIM Proc. Surveys, 62(2018): 68–78. |
[13] | P. Gwiazda, T. Lorenz and A. Marciniak-Czochra, A nonlinear structured population model: Lipschitz continuity of measure-valued solutions with respect to model ingredients, J. Differ. Equ., 248(2010): 2703–2735. |
[14] | P. Gabriel, S. P. Garbett, V. Quaranta et al., The contribution of age structure to cell population responses to targeted therapeutics, J. Theor. Biol., 311(2012): 19–27. |
[15] | A. Perasso and U. Razafison, Identifiability problem for recovering the mortality rate in an agestructured population dynamics model, Inverse Probl. Sci. Eng., 24(2016): 711–728. |
[16] | B. Perthame and J. P. Zubelli, On the inverse problem for a size-structured population model. Inverse Problems, 23(2007): 1037. |
[17] | M. Doumic, B. Perthame and J. P. Zubelli, Numerical solution of an inverse problem in sizestructured population dynamics, Inverse Problems, 25(2009): 045008. |
[18] | T. Bourgeron, M. Doumic and M. Escobedo, Estimating the division rate of the growthfragmentation equation with a self-similar kernel, Inverse Problems, 30(2014): 025007. |
[19] | M. Iannelli, T. Kostova and F. Augusto Milner, A fourthorder method for numerical integration of age and sizestructured population models, Numer. Methods Partial. Differ. Equ., 25(2009): 918–930. |