 Previous Article
 KRM Home
 This Issue

Next Article
Convergence rates towards the traveling waves for a model system of radiating gas with discontinuities
An agestructured twosex model in the space of radon measures: Well posedness
1.  University of Warsaw, ul. Banacha 2, 02097 Warsaw, Poland 
References:
[1] 
L. Ambrosio, N. Gigli and G. Savaré, "Gradient Flows in Metric Spaces and in the Space of Probability Measures," Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 2005. 
[2] 
J. A. Cañizo, J. A. Carrillo and S. Cuadrado, Measure solutions for some models in population dynamics, Acta Applicandae Mathematicae, (2012), 116. 
[3] 
J. A. Carrillo, R. M. Colombo, P. Gwiazda and A. Ulikowska, Structured populations, cell growth and measure valued balance laws, Journal of Differential Equations, 252 (2012), 32453277. 
[4] 
C. CastilloChávez and W. Huang, The logistic equation revisited, Math. Biosci., 128 (1995), 199316. 
[5] 
O. Diekmann and J.A.J. Metz, "The dynamics of Physiologically Structured populations," Lecture Notes in Biomathematics, 68, SpringerVerlag, Berlin, 1986. 
[6] 
K. Dietz and K. P. Hadeler, Epidemiological models for sexually transmitted diseases, J. Math. Biol., 26 (1988), 125. 
[7] 
L. C. Evans, "Weak Convergence Methods for Nonlinear Partial Differential Equations," CBMS Regional Conference Series in Mathematics, 74, published for the Conference Board of the Mathematical Sciences, Washington, DC, 1990. 
[8] 
L. C. Evans, "Partial Differential Equations," Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, RI, 2010. 
[9] 
A. Fredrickson, A mathematical theory of age structure in sexual populations: random mating and monogamous models, Math. Biosci., 10 (1971), 117143. doi: 10.1016/00255564(71)90054X. 
[10] 
A. Fredrickson and P. Hsu, Populationchanging processes and the dynamics of sexual populations, Math. Biosci., 26 (1975), 5578. doi: 10.1016/00255564(75)900942. 
[11] 
G. Garnett, An introduction to mathematical models in sexually transmitted disease epidemiology, Sex Transm. Inf., 78 (2001), 712. 
[12] 
P. Gwiazda, G. Jamróz and A. MarciniakCzochra, Models of discrete and continuous cell differentiation in the framework of transport equation, SIAM J. Math. Anal., 44 (2012), 11031133. 
[13] 
P. Gwiazda, T. Lorenz and A. MarciniakCzochra, A nonlinear structured population model: Lipschitz continuity of measurevalued solutions with respect to model ingredients, Journal of Differential Equations, 248 (2010), 27032735. 
[14] 
P. Gwiazda and A. MarciniakCzochra, Structured population equations in metric spaces, J. Hyperbolic Differ. Equ., 7 2010, 733773. 
[15] 
K. Hadeler and K. Ngoma, Homogeneous models for sexually transmitted diseases, Rocky Mt. J. Math., 20 (1990), 967986. 
[16] 
K. P. Hadeler, Pair formation in agestructured populations, Acta Appl. Math., 14 (1989), 91102. 
[17] 
K. P. Hadeler, R. Waldstätter and A. WörzBusekros, Models for pair formation in bisexual populations, J. Math. Biol., 26 (1988), 635649. doi: 10.1007/BF00276145. 
[18] 
F. Hoppensteadt, "Mathematical Theories of Populations: Demographics, Genetics and Epidemics," Society for Industrial and Applied Mathematics, Philadelphia, PA, 1975. 
[19] 
M. Iannelli, M. Martcheva and F. A. Milner, "Genderstructured Population Modeling. Mathematical Methods, Numerics, and Simulations," Frontiers in Applied Mathematics, 31, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2005. 
[20] 
H. Inaba, "An Agestructured Twosex Model for Human Population Reproduction by First Marriage," volume 15 of Working paper series, Institute of Population Problems, Tokyo, 1993. 
[21] 
H. Inaba, Persistent age distributions for an agestructured twosex population model, Math. Population Studies, 7 (2000), 365398. 
[22] 
D. G. Kendall, Stochastic processes and population growth, J. Roy. Statist. Soc. Ser. B., 11 (1949), 230264. 
[23] 
M. Martcheva, Exponential growth in agestructured twosex populations, Math. Biosci., 157 (1999), 122. 
[24] 
M. Martcheva and F. A. Milner, A twosex agestructured population model: well posedness, Math. Population Stud., 7 (1999), 111129. 
[25] 
M. Martcheva and F. A. Milner, The mathematics of sex and marriage, revisited, Math. Population Stud., 9 (2001), 123141. 
[26] 
D. Maxin and F. Milner, The effect of nonreproductive groups on persistent sexually transmitted diseases, Math. Biosc. and Engin., 4 (2007), 505522. doi: 10.3934/mbe.2007.4.505. 
[27] 
F. Milner and K. Yang, The logistic, twosex, agestructured population model, J. Biol. Dyn., 3 (2009), 252270. 
[28] 
J. Prüss and W. Schappacher, Persistent agedistributions for a pairformation model, J. Math. Biol., 33 (1994), 1733. 
[29] 
G. F. Webb, "Structured Population Dynamics," Banach Center Publications, 63, Polish Acad. Sci., Warsaw, 2004. 
show all references
References:
[1] 
L. Ambrosio, N. Gigli and G. Savaré, "Gradient Flows in Metric Spaces and in the Space of Probability Measures," Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 2005. 
[2] 
J. A. Cañizo, J. A. Carrillo and S. Cuadrado, Measure solutions for some models in population dynamics, Acta Applicandae Mathematicae, (2012), 116. 
[3] 
J. A. Carrillo, R. M. Colombo, P. Gwiazda and A. Ulikowska, Structured populations, cell growth and measure valued balance laws, Journal of Differential Equations, 252 (2012), 32453277. 
[4] 
C. CastilloChávez and W. Huang, The logistic equation revisited, Math. Biosci., 128 (1995), 199316. 
[5] 
O. Diekmann and J.A.J. Metz, "The dynamics of Physiologically Structured populations," Lecture Notes in Biomathematics, 68, SpringerVerlag, Berlin, 1986. 
[6] 
K. Dietz and K. P. Hadeler, Epidemiological models for sexually transmitted diseases, J. Math. Biol., 26 (1988), 125. 
[7] 
L. C. Evans, "Weak Convergence Methods for Nonlinear Partial Differential Equations," CBMS Regional Conference Series in Mathematics, 74, published for the Conference Board of the Mathematical Sciences, Washington, DC, 1990. 
[8] 
L. C. Evans, "Partial Differential Equations," Graduate Studies in Mathematics, 19, American Mathematical Society, Providence, RI, 2010. 
[9] 
A. Fredrickson, A mathematical theory of age structure in sexual populations: random mating and monogamous models, Math. Biosci., 10 (1971), 117143. doi: 10.1016/00255564(71)90054X. 
[10] 
A. Fredrickson and P. Hsu, Populationchanging processes and the dynamics of sexual populations, Math. Biosci., 26 (1975), 5578. doi: 10.1016/00255564(75)900942. 
[11] 
G. Garnett, An introduction to mathematical models in sexually transmitted disease epidemiology, Sex Transm. Inf., 78 (2001), 712. 
[12] 
P. Gwiazda, G. Jamróz and A. MarciniakCzochra, Models of discrete and continuous cell differentiation in the framework of transport equation, SIAM J. Math. Anal., 44 (2012), 11031133. 
[13] 
P. Gwiazda, T. Lorenz and A. MarciniakCzochra, A nonlinear structured population model: Lipschitz continuity of measurevalued solutions with respect to model ingredients, Journal of Differential Equations, 248 (2010), 27032735. 
[14] 
P. Gwiazda and A. MarciniakCzochra, Structured population equations in metric spaces, J. Hyperbolic Differ. Equ., 7 2010, 733773. 
[15] 
K. Hadeler and K. Ngoma, Homogeneous models for sexually transmitted diseases, Rocky Mt. J. Math., 20 (1990), 967986. 
[16] 
K. P. Hadeler, Pair formation in agestructured populations, Acta Appl. Math., 14 (1989), 91102. 
[17] 
K. P. Hadeler, R. Waldstätter and A. WörzBusekros, Models for pair formation in bisexual populations, J. Math. Biol., 26 (1988), 635649. doi: 10.1007/BF00276145. 
[18] 
F. Hoppensteadt, "Mathematical Theories of Populations: Demographics, Genetics and Epidemics," Society for Industrial and Applied Mathematics, Philadelphia, PA, 1975. 
[19] 
M. Iannelli, M. Martcheva and F. A. Milner, "Genderstructured Population Modeling. Mathematical Methods, Numerics, and Simulations," Frontiers in Applied Mathematics, 31, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2005. 
[20] 
H. Inaba, "An Agestructured Twosex Model for Human Population Reproduction by First Marriage," volume 15 of Working paper series, Institute of Population Problems, Tokyo, 1993. 
[21] 
H. Inaba, Persistent age distributions for an agestructured twosex population model, Math. Population Studies, 7 (2000), 365398. 
[22] 
D. G. Kendall, Stochastic processes and population growth, J. Roy. Statist. Soc. Ser. B., 11 (1949), 230264. 
[23] 
M. Martcheva, Exponential growth in agestructured twosex populations, Math. Biosci., 157 (1999), 122. 
[24] 
M. Martcheva and F. A. Milner, A twosex agestructured population model: well posedness, Math. Population Stud., 7 (1999), 111129. 
[25] 
M. Martcheva and F. A. Milner, The mathematics of sex and marriage, revisited, Math. Population Stud., 9 (2001), 123141. 
[26] 
D. Maxin and F. Milner, The effect of nonreproductive groups on persistent sexually transmitted diseases, Math. Biosc. and Engin., 4 (2007), 505522. doi: 10.3934/mbe.2007.4.505. 
[27] 
F. Milner and K. Yang, The logistic, twosex, agestructured population model, J. Biol. Dyn., 3 (2009), 252270. 
[28] 
J. Prüss and W. Schappacher, Persistent agedistributions for a pairformation model, J. Math. Biol., 33 (1994), 1733. 
[29] 
G. F. Webb, "Structured Population Dynamics," Banach Center Publications, 63, Polish Acad. Sci., Warsaw, 2004. 
[1] 
Yacouba Simporé, Oumar Traoré. Null controllability of a nonlinear age, space and twosex structured population dynamics model. Mathematical Control and Related Fields, 2021 doi: 10.3934/mcrf.2021052 
[2] 
Anthony Tongen, María Zubillaga, Jorge E. Rabinovich. A twosex matrix population model to represent harem structure. Mathematical Biosciences & Engineering, 2016, 13 (5) : 10771092. doi: 10.3934/mbe.2016031 
[3] 
Xianlong Fu, Zhihua Liu, Pierre Magal. Hopf bifurcation in an agestructured population model with two delays. Communications on Pure and Applied Analysis, 2015, 14 (2) : 657676. doi: 10.3934/cpaa.2015.14.657 
[4] 
Z.R. He, M.S. Wang, Z.E. Ma. Optimal birth control problems for nonlinear agestructured population dynamics. Discrete and Continuous Dynamical Systems  B, 2004, 4 (3) : 589594. doi: 10.3934/dcdsb.2004.4.589 
[5] 
Frédérique Billy, Jean Clairambault, Franck Delaunay, Céline Feillet, Natalia Robert. Agestructured cell population model to study the influence of growth factors on cell cycle dynamics. Mathematical Biosciences & Engineering, 2013, 10 (1) : 117. doi: 10.3934/mbe.2013.10.1 
[6] 
Linlin Li, Bedreddine Ainseba. Largetime behavior of matured population in an agestructured model. Discrete and Continuous Dynamical Systems  B, 2021, 26 (5) : 25612580. doi: 10.3934/dcdsb.2020195 
[7] 
Diène Ngom, A. Iggidir, Aboudramane Guiro, Abderrahim Ouahbi. An observer for a nonlinear agestructured model of a harvested fish population. Mathematical Biosciences & Engineering, 2008, 5 (2) : 337354. doi: 10.3934/mbe.2008.5.337 
[8] 
Azmy S. Ackleh, Vinodh K. Chellamuthu, Kazufumi Ito. Finite difference approximations for measurevalued solutions of a hierarchically sizestructured population model. Mathematical Biosciences & Engineering, 2015, 12 (2) : 233258. doi: 10.3934/mbe.2015.12.233 
[9] 
Zhihua Liu, Hui Tang, Pierre Magal. Hopf bifurcation for a spatially and age structured population dynamics model. Discrete and Continuous Dynamical Systems  B, 2015, 20 (6) : 17351757. doi: 10.3934/dcdsb.2015.20.1735 
[10] 
Sebastian Aniţa, AnaMaria Moşsneagu. Optimal harvesting for agestructured population dynamics with sizedependent control. Mathematical Control and Related Fields, 2019, 9 (4) : 607621. doi: 10.3934/mcrf.2019043 
[11] 
Guangrui Li, Ming Mei, Yau Shu Wong. Nonlinear stability of traveling wavefronts in an agestructured reactiondiffusion population model. Mathematical Biosciences & Engineering, 2008, 5 (1) : 85100. doi: 10.3934/mbe.2008.5.85 
[12] 
Mohammed Nor Frioui, Tarik Mohammed Touaoula, Bedreddine Ainseba. Global dynamics of an agestructured model with relapse. Discrete and Continuous Dynamical Systems  B, 2020, 25 (6) : 22452270. doi: 10.3934/dcdsb.2019226 
[13] 
Fred Brauer. A model for an SI disease in an age  structured population. Discrete and Continuous Dynamical Systems  B, 2002, 2 (2) : 257264. doi: 10.3934/dcdsb.2002.2.257 
[14] 
Jacques Henry. For which objective is birth process an optimal feedback in age structured population dynamics?. Discrete and Continuous Dynamical Systems  B, 2007, 8 (1) : 107114. doi: 10.3934/dcdsb.2007.8.107 
[15] 
Tristan Roget. On the longtime behaviour of age and trait structured population dynamics. Discrete and Continuous Dynamical Systems  B, 2019, 24 (6) : 25512576. doi: 10.3934/dcdsb.2018265 
[16] 
Georgi Kapitanov, Christina Alvey, Katia VogtGeisse, Zhilan Feng. An agestructured model for the coupled dynamics of HIV and HSV2. Mathematical Biosciences & Engineering, 2015, 12 (4) : 803840. doi: 10.3934/mbe.2015.12.803 
[17] 
Xichao Duan, Sanling Yuan, Kaifa Wang. Dynamics of a diffusive agestructured HBV model with saturating incidence. Mathematical Biosciences & Engineering, 2016, 13 (5) : 935968. doi: 10.3934/mbe.2016024 
[18] 
G. Buffoni, S. Pasquali, G. Gilioli. A stochastic model for the dynamics of a stage structured population. Discrete and Continuous Dynamical Systems  B, 2004, 4 (3) : 517525. doi: 10.3934/dcdsb.2004.4.517 
[19] 
Peixuan Weng. Spreading speed and traveling wavefront of an agestructured population diffusing in a 2D lattice strip. Discrete and Continuous Dynamical Systems  B, 2009, 12 (4) : 883904. doi: 10.3934/dcdsb.2009.12.883 
[20] 
Yingli Pan, Ying Su, Junjie Wei. Bistable waves of a recursive system arising from seasonal agestructured population models. Discrete and Continuous Dynamical Systems  B, 2019, 24 (2) : 511528. doi: 10.3934/dcdsb.2018184 
2020 Impact Factor: 1.432
Tools
Metrics
Other articles
by authors
[Back to Top]