-
Previous Article
Global attracting set, exponential decay and stability in distribution of neutral SPDEs driven by additive $\alpha$-stable processes
- DCDS-B Home
- This Issue
-
Next Article
The vanishing surface tension limit for the Hele-Shaw problem
A multi-group SIR epidemic model with age structure
1. | Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-0067, Japan |
2. | School of Mathematical Science, Heilongjiang University, Harbin 150080 |
3. | Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba Meguro-ku, Tokyo 153-8914 |
References:
[1] |
in Mathematical Population Dynamics: Analysis of Heterogeneity (eds. O. Arino, D. Axelrod, M. Kimmel and M. Langlais), Wuerz Publ., (1995), 3-14. Google Scholar |
[2] |
in Mathematical Ecology (eds. T.G. Hallam, L.J. Gross and S.A. Levin), World Scientific, (1988), 317-342. |
[3] |
SIAM J. Math. Anal., 22 (1991), 1065-1080.
doi: 10.1137/0522069. |
[4] |
Dynam. Syst. Appl., 9 (2000), 361-376. |
[5] |
J. Math. Biol., 28 (1990), 365-382.
doi: 10.1007/BF00178324. |
[6] |
Princeton University Press, Princeton and Oxford, 2013. |
[7] |
in Proc. SIMS Conf. on Epidemiology (eds. D. Ludwig and K.L. Cooke), SIAM, (1975), 104-121. Google Scholar |
[8] |
J. Diff. Equat., 218 (2005), 292-324.
doi: 10.1016/j.jde.2004.10.009. |
[9] |
Math. Biosci. Eng., 9 (2012), 577-599.
doi: 10.3934/mbe.2012.9.577. |
[10] |
IMA J. Math. Appl. Med. Biol., 4 (1987), 109-144.
doi: 10.1093/imammb/4.2.109. |
[11] |
J. reine angew. Math., 341 (1983), 54-67.
doi: 10.1515/crll.1983.341.54. |
[12] |
Canadian Appl. Math. Quart., 14 (2006), 259-284. |
[13] |
in The Dynamics of Physiologically Structured Populations (eds. J.A.J. Metz and O. Diekmann), Springer, 68 (1986), 185-202.
doi: 10.1007/978-3-662-13159-6_5. |
[14] |
Theor. Popul. Biol., 14 (1978), 338-349.
doi: 10.1016/0040-5809(78)90011-4. |
[15] |
SIAM Review, 42 (2000), 599-653.
doi: 10.1137/S0036144500371907. |
[16] |
J. Franklin Inst., 297 (1974), 325-333.
doi: 10.1016/0016-0032(74)90037-4. |
[17] |
Math. Popul. Studies, 1 (1988), 49-77.
doi: 10.1080/08898488809525260. |
[18] |
J. Math. Biol., 28 (1990), 411-434.
doi: 10.1007/BF00178326. |
[19] |
Math. Biosci., 201 (2006), 15-47.
doi: 10.1016/j.mbs.2005.12.017. |
[20] |
Math. Model. Nat. Phenom., 3 (2008), 194-228.
doi: 10.1051/mmnp:2008050. |
[21] |
Math. Biosci. Eng., 9 (2012), 313-346.
doi: 10.3934/mbe.2012.9.313. |
[22] |
J. Math. Biol., 65 (2012), 309-348.
doi: 10.1007/s00285-011-0463-z. |
[23] |
2nd edition, Springer, Berlin, 1995. |
[24] |
Nonlinear Analysis RWA., 9 (2008), 1989-2028.
doi: 10.1016/j.nonrwa.2007.06.004. |
[25] |
Bull. Math. Biol., 71 (2009), 75-83.
doi: 10.1007/s11538-008-9352-z. |
[26] |
1st edition, Noordhoff, Groningen, 1964. |
[27] |
Am. Math. Soc. Transl., 1950 (1950), 128pp. |
[28] |
Nonlinear Analysis RWA., 12 (2011), 2640-2655.
doi: 10.1016/j.nonrwa.2011.03.011. |
[29] |
2nd edition, SIAM, Philadelphia, 1976. |
[30] |
Math. Biosci. Eng., 7 (2010), 123-147.
doi: 10.3934/mbe.2010.7.123. |
[31] |
Appl. Anal., 89 (2010), 1109-1140.
doi: 10.1080/00036810903208122. |
[32] |
SIAM J. Appl. Math., 19 (1970), 607-628.
doi: 10.1137/0119060. |
[33] |
Math. Biosci. Eng., 9 (2012), 819-841.
doi: 10.3934/mbe.2012.9.819. |
[34] |
Proc. Edinburgh Math. Soc., (1925), 98-130.
doi: 10.1017/S0013091500034428. |
[35] |
Math. Biosci. Eng., 10 (2013), 369-378.
doi: 10.3934/mbe.2013.10.369. |
[36] |
1st edition, Springer, Berlin, 1986.
doi: 10.1007/BFb0074922. |
[37] |
Nat. Sci. Rep. Ochanomizu Univ., 15 (1964), 53-64. |
[38] |
1st edition, Amer. Math. Soc., Providence, 2011. |
[39] |
Comput. Math. Appl., 60 (2010), 2286-2291.
doi: 10.1016/j.camwa.2010.08.020. |
[40] |
in Differential Equations Models in Biology, Epidemiology and Ecology (eds. S. Busenberg and M. Martelli), Springer, 92 (1991), 139-158.
doi: 10.1007/978-3-642-45692-3_10. |
[41] |
Math. Biosci., 73 (1985), 131-147.
doi: 10.1016/0025-5564(85)90081-1. |
[42] |
Theor. Popul. Biol., 40 (1991), 322-353.
doi: 10.1016/0040-5809(91)90059-O. |
[43] |
Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[44] |
1st edition, Plenum Press, New York and London, 1980. |
[45] |
J. Biol. Syst., 20 (2012), 235-258.
doi: 10.1142/S021833901250009X. |
[46] |
1st edition, Marcel Dekker, New York and Basel, 1985. |
[47] |
6th edition, Springer, Berlin, 1980. |
show all references
References:
[1] |
in Mathematical Population Dynamics: Analysis of Heterogeneity (eds. O. Arino, D. Axelrod, M. Kimmel and M. Langlais), Wuerz Publ., (1995), 3-14. Google Scholar |
[2] |
in Mathematical Ecology (eds. T.G. Hallam, L.J. Gross and S.A. Levin), World Scientific, (1988), 317-342. |
[3] |
SIAM J. Math. Anal., 22 (1991), 1065-1080.
doi: 10.1137/0522069. |
[4] |
Dynam. Syst. Appl., 9 (2000), 361-376. |
[5] |
J. Math. Biol., 28 (1990), 365-382.
doi: 10.1007/BF00178324. |
[6] |
Princeton University Press, Princeton and Oxford, 2013. |
[7] |
in Proc. SIMS Conf. on Epidemiology (eds. D. Ludwig and K.L. Cooke), SIAM, (1975), 104-121. Google Scholar |
[8] |
J. Diff. Equat., 218 (2005), 292-324.
doi: 10.1016/j.jde.2004.10.009. |
[9] |
Math. Biosci. Eng., 9 (2012), 577-599.
doi: 10.3934/mbe.2012.9.577. |
[10] |
IMA J. Math. Appl. Med. Biol., 4 (1987), 109-144.
doi: 10.1093/imammb/4.2.109. |
[11] |
J. reine angew. Math., 341 (1983), 54-67.
doi: 10.1515/crll.1983.341.54. |
[12] |
Canadian Appl. Math. Quart., 14 (2006), 259-284. |
[13] |
in The Dynamics of Physiologically Structured Populations (eds. J.A.J. Metz and O. Diekmann), Springer, 68 (1986), 185-202.
doi: 10.1007/978-3-662-13159-6_5. |
[14] |
Theor. Popul. Biol., 14 (1978), 338-349.
doi: 10.1016/0040-5809(78)90011-4. |
[15] |
SIAM Review, 42 (2000), 599-653.
doi: 10.1137/S0036144500371907. |
[16] |
J. Franklin Inst., 297 (1974), 325-333.
doi: 10.1016/0016-0032(74)90037-4. |
[17] |
Math. Popul. Studies, 1 (1988), 49-77.
doi: 10.1080/08898488809525260. |
[18] |
J. Math. Biol., 28 (1990), 411-434.
doi: 10.1007/BF00178326. |
[19] |
Math. Biosci., 201 (2006), 15-47.
doi: 10.1016/j.mbs.2005.12.017. |
[20] |
Math. Model. Nat. Phenom., 3 (2008), 194-228.
doi: 10.1051/mmnp:2008050. |
[21] |
Math. Biosci. Eng., 9 (2012), 313-346.
doi: 10.3934/mbe.2012.9.313. |
[22] |
J. Math. Biol., 65 (2012), 309-348.
doi: 10.1007/s00285-011-0463-z. |
[23] |
2nd edition, Springer, Berlin, 1995. |
[24] |
Nonlinear Analysis RWA., 9 (2008), 1989-2028.
doi: 10.1016/j.nonrwa.2007.06.004. |
[25] |
Bull. Math. Biol., 71 (2009), 75-83.
doi: 10.1007/s11538-008-9352-z. |
[26] |
1st edition, Noordhoff, Groningen, 1964. |
[27] |
Am. Math. Soc. Transl., 1950 (1950), 128pp. |
[28] |
Nonlinear Analysis RWA., 12 (2011), 2640-2655.
doi: 10.1016/j.nonrwa.2011.03.011. |
[29] |
2nd edition, SIAM, Philadelphia, 1976. |
[30] |
Math. Biosci. Eng., 7 (2010), 123-147.
doi: 10.3934/mbe.2010.7.123. |
[31] |
Appl. Anal., 89 (2010), 1109-1140.
doi: 10.1080/00036810903208122. |
[32] |
SIAM J. Appl. Math., 19 (1970), 607-628.
doi: 10.1137/0119060. |
[33] |
Math. Biosci. Eng., 9 (2012), 819-841.
doi: 10.3934/mbe.2012.9.819. |
[34] |
Proc. Edinburgh Math. Soc., (1925), 98-130.
doi: 10.1017/S0013091500034428. |
[35] |
Math. Biosci. Eng., 10 (2013), 369-378.
doi: 10.3934/mbe.2013.10.369. |
[36] |
1st edition, Springer, Berlin, 1986.
doi: 10.1007/BFb0074922. |
[37] |
Nat. Sci. Rep. Ochanomizu Univ., 15 (1964), 53-64. |
[38] |
1st edition, Amer. Math. Soc., Providence, 2011. |
[39] |
Comput. Math. Appl., 60 (2010), 2286-2291.
doi: 10.1016/j.camwa.2010.08.020. |
[40] |
in Differential Equations Models in Biology, Epidemiology and Ecology (eds. S. Busenberg and M. Martelli), Springer, 92 (1991), 139-158.
doi: 10.1007/978-3-642-45692-3_10. |
[41] |
Math. Biosci., 73 (1985), 131-147.
doi: 10.1016/0025-5564(85)90081-1. |
[42] |
Theor. Popul. Biol., 40 (1991), 322-353.
doi: 10.1016/0040-5809(91)90059-O. |
[43] |
Math. Biosci., 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[44] |
1st edition, Plenum Press, New York and London, 1980. |
[45] |
J. Biol. Syst., 20 (2012), 235-258.
doi: 10.1142/S021833901250009X. |
[46] |
1st edition, Marcel Dekker, New York and Basel, 1985. |
[47] |
6th edition, Springer, Berlin, 1980. |
[1] |
Jing Feng, Bin-Guo Wang. An almost periodic Dengue transmission model with age structure and time-delayed input of vector in a patchy environment. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3069-3096. doi: 10.3934/dcdsb.2020220 |
[2] |
Linlin Li, Bedreddine Ainseba. Large-time behavior of matured population in an age-structured model. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2561-2580. doi: 10.3934/dcdsb.2020195 |
[3] |
Shangzhi Li, Shangjiang Guo. Permanence and extinction of a stochastic SIS epidemic model with three independent Brownian motions. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2693-2719. doi: 10.3934/dcdsb.2020201 |
[4] |
Renhao Cui. Asymptotic profiles of the endemic equilibrium of a reaction-diffusion-advection SIS epidemic model with saturated incidence rate. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 2997-3022. doi: 10.3934/dcdsb.2020217 |
[5] |
Yuta Ishii, Kazuhiro Kurata. Existence of multi-peak solutions to the Schnakenberg model with heterogeneity on metric graphs. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021035 |
[6] |
Haodong Chen, Hongchun Sun, Yiju Wang. A complementarity model and algorithm for direct multi-commodity flow supply chain network equilibrium problem. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2217-2242. doi: 10.3934/jimo.2020066 |
[7] |
Hideaki Takagi. Extension of Littlewood's rule to the multi-period static revenue management model with standby customers. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2181-2202. doi: 10.3934/jimo.2020064 |
[8] |
Ru Li, Guolin Yu. Strict efficiency of a multi-product supply-demand network equilibrium model. Journal of Industrial & Management Optimization, 2021, 17 (4) : 2203-2215. doi: 10.3934/jimo.2020065 |
[9] |
Prabir Panja, Soovoojeet Jana, Shyamal kumar Mondal. Dynamics of a stage structure prey-predator model with ratio-dependent functional response and anti-predator behavior of adult prey. Numerical Algebra, Control & Optimization, 2021, 11 (3) : 391-405. doi: 10.3934/naco.2020033 |
[10] |
Jan Prüss, Laurent Pujo-Menjouet, G.F. Webb, Rico Zacher. Analysis of a model for the dynamics of prions. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 225-235. doi: 10.3934/dcdsb.2006.6.225 |
[11] |
Johannes Kellendonk, Lorenzo Sadun. Conjugacies of model sets. Discrete & Continuous Dynamical Systems, 2017, 37 (7) : 3805-3830. doi: 10.3934/dcds.2017161 |
[12] |
Didier Bresch, Thierry Colin, Emmanuel Grenier, Benjamin Ribba, Olivier Saut. A viscoelastic model for avascular tumor growth. Conference Publications, 2009, 2009 (Special) : 101-108. doi: 10.3934/proc.2009.2009.101 |
[13] |
Ondrej Budáč, Michael Herrmann, Barbara Niethammer, Andrej Spielmann. On a model for mass aggregation with maximal size. Kinetic & Related Models, 2011, 4 (2) : 427-439. doi: 10.3934/krm.2011.4.427 |
[14] |
Thomas Alazard. A minicourse on the low Mach number limit. Discrete & Continuous Dynamical Systems - S, 2008, 1 (3) : 365-404. doi: 10.3934/dcdss.2008.1.365 |
[15] |
Dandan Cheng, Qian Hao, Zhiming Li. Scale pressure for amenable group actions. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1091-1102. doi: 10.3934/cpaa.2021008 |
[16] |
Martin Bohner, Sabrina Streipert. Optimal harvesting policy for the Beverton--Holt model. Mathematical Biosciences & Engineering, 2016, 13 (4) : 673-695. doi: 10.3934/mbe.2016014 |
[17] |
Juan Manuel Pastor, Javier García-Algarra, Javier Galeano, José María Iriondo, José J. Ramasco. A simple and bounded model of population dynamics for mutualistic networks. Networks & Heterogeneous Media, 2015, 10 (1) : 53-70. doi: 10.3934/nhm.2015.10.53 |
[18] |
Chin-Chin Wu. Existence of traveling wavefront for discrete bistable competition model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 973-984. doi: 10.3934/dcdsb.2011.16.973 |
[19] |
Michael Grinfeld, Amy Novick-Cohen. Some remarks on stability for a phase field model with memory. Discrete & Continuous Dynamical Systems, 2006, 15 (4) : 1089-1117. doi: 10.3934/dcds.2006.15.1089 |
[20] |
Alba Málaga Sabogal, Serge Troubetzkoy. Minimality of the Ehrenfest wind-tree model. Journal of Modern Dynamics, 2016, 10: 209-228. doi: 10.3934/jmd.2016.10.209 |
2019 Impact Factor: 1.27
Tools
Metrics
Other articles
by authors
[Back to Top]