A celebration of Fred Brauer's legacy in mathematical biology.
Biography
Pandemic preparedness
Predator–prey systems
Retrospective
Journal
Journal of mathematical biology
ISSN: 1432-1416
Titre abrégé: J Math Biol
Pays: Germany
ID NLM: 7502105
Informations de publication
Date de publication:
03 08 2023
03 08 2023
Historique:
received:
13
06
2023
accepted:
30
06
2023
revised:
13
06
2023
medline:
7
8
2023
pubmed:
4
8
2023
entrez:
3
8
2023
Statut:
epublish
Résumé
Fred Brauer (1932-2021), one of the pioneers of mathematical population biology, shaped generations of researchers through his lines of research, his books which have become key references in the field, and his mentoring of junior researchers. This dedication reviews some of his work in population harvesting and epidemiological modeling, highlighting how this special collection reflects the impact of his legacy through both his research accomplishments and the formation of new researchers.
Identifiants
pubmed: 37537314
doi: 10.1007/s00285-023-01971-z
pii: 10.1007/s00285-023-01971-z
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
37Informations de copyright
© 2023. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Références
Arino J, Brauer F, van den Driessche P, Watmough J, Wu J (2006) Simple models for containment of a pandemic. J. R Soc Interface 3(8):453–457. https://doi.org/10.1098/rsif.2006.0112
doi: 10.1098/rsif.2006.0112
Bai F, Brauer F (2021) The effect of face mask use on COVID-19 models. Epidemiologia 2(1):75–83
doi: 10.3390/epidemiologia2010007
Beddington JR, May RM (1980) Maximum sustainable yields in systems subject to harvesting at more than one trophic level. Math Biosci 51:261–281
doi: 10.1016/0025-5564(80)90103-0
Brauer F (1976a) Constant-rate harvesting of populations governed by Volterra integral equations. J Math Anal Appl 56:18–27
doi: 10.1016/0022-247X(76)90004-4
Brauer F (1976b) Perturbations of the nonlinear renewal equation. Adv Math 22:32–51
doi: 10.1016/0001-8708(76)90136-5
Brauer F (1977) Stability of some population models with delay. Math Biosci 33:345–358
doi: 10.1016/0025-5564(77)90148-1
Brauer F (1983a) Constant-rate harvested of age-structured populations. SIAM J Math Anal 14:947–961
doi: 10.1137/0514074
Brauer F (1983b) Nonlinear age-dependent population growth under harvesting. Comput Math Appl 9:345–352
doi: 10.1016/0898-1221(83)90022-6
Brauer F (2004) Backward bifurcations in simple vaccination models. J Math Anal Appl 298(2):418–431
doi: 10.1016/j.jmaa.2004.05.045
Brauer F (2008) Compartmental models in epidemiology. In: Brauer F, van den Driessche P, Allen LJS (eds) Mathematical epidemiology. Heidelberg, Springer, pp 19–79
doi: 10.1007/978-3-540-78911-6_2
Brauer F (2017) Mathematical epidemiology: past, present, and future. Infect Dis Model 2(2):113–127
Brauer F (2019a) The final size of a serious epidemic. Bull Math Biol 81(3):869–877
doi: 10.1007/s11538-018-00549-x
Brauer F (2019b) Early estimates of epidemic final sizes. J Biol Dyn 13(sup1):23–30
doi: 10.1080/17513758.2018.1469792
Brauer F (2019c) A singular perturbation approach to epidemics of vector-transmitted diseases. Infect Dis Model 4:115–123
Brauer F (2019d) The final size of a serious epidemic. Bull Math Biol 81:869–877. https://doi.org/10.1007/s11538-018-00549-x
doi: 10.1007/s11538-018-00549-x
Brauer F, Castillo-Chavez C (2012) Mathematical models in population biology and epidemiology, 2nd edn. Springer, New York
doi: 10.1007/978-1-4614-1686-9
Brauer F, Kribs C (2015) Dynamical systems for biological modeling: an introduction. CRC Press/Taylor & Francis, Boca Raton
doi: 10.1201/b20687
Brauer F, Sánchez DA (1975) Constant rate population harvesting: equilibrium and stability. Theor Pop Biol 8:12–30
doi: 10.1016/0040-5809(75)90036-2
Brauer F, Sánchez DA (2003) Periodic environments and periodic harvesting. Nat Resour Model 16:233–244
doi: 10.1111/j.1939-7445.2003.tb00113.x
Brauer F, Soudack AC (1979a) Stability regions and transition phenomena for harvested predator-prey systems. J Math Biol 7:319–337
doi: 10.1007/BF00275152
Brauer F, Soudack AC (1979b) Stability regions in predator-prey systems with constant-rate prey harvesting. J Math Biol 8:55–71
doi: 10.1007/BF00280586
Brauer F, Soudack AC (1981a) Constant-rate stocking of predator-prey systems. J Math Biol 11:1–14
doi: 10.1007/BF00275820
Brauer F, Soudack AC (1981b) Coexistence properties of some predator-prey systems under constant rate harvesting and stocking. J Math Biol 12:101–114
doi: 10.1007/BF00275206
Brauer F, Soudack AC, Jarosch HS (1976) Stabilization and de-stabilization of predator-prey systems under harvesting and nutrient enrichment. Int J Control 23:553–573
doi: 10.1080/00207177608922181
Brauer F, Rollins D, Soudack AC (1988) Harvesting in population models with delayed recruitment and age-dependent mortality rate. Nat Resour Model 3:45–62
doi: 10.1111/j.1939-7445.1988.tb00057.x
Brauer F, van den Driessche P, Allen LJS (2008) Mathematical epidemiology. Ed. J. Wu. Lecture Notes, vol 1945. Springer, Berlin
Brauer F, Castillo-Chavez C, Feng Z (2019) Mathematical models in epidemiology. Texts in applied mathematics, vol 32. Springer, New York
David JF, Iyaniwura SA, Ward MJ, Brauer F (2020a) A novel approach to modelling the spatial spread of airborne diseases: an epidemic model with indirect transmission. Math Biosci Eng 17(4):3294–3328
doi: 10.3934/mbe.2020188
David JF, Lima VD, Zhu J, Brauer F (2020b) A co-interaction model of HIV and syphilis infection among gay, bisexual and other men who have sex with men. Infect Dis Model 5:855–870
Davoudi B, Moser F, Brauer F, Pourbohloul B (2013) Epidemic progression on networks based on disease generation time. J Biol Dyn 7(1):148–160. https://doi.org/10.1080/17513758.2013.819127
doi: 10.1080/17513758.2013.819127
Lazer AC, Sánchez DA (1984) Periodic equilibria under periodic harvesting. Math Mag 57:156–158
doi: 10.1080/0025570X.1984.11977098
May R, Beddington JR, Clark CW, Holt SJ, Laws RM (1979) Management of multispecies fisheries. Science 205:267–277
doi: 10.1126/science.205.4403.267
Ortigoza G, Brauer F, Lorandi A (2019) Mosquito-borne diseases simulated by cellular automata: A review. Int J Mosquito Res 6(6):31–38
Ortigoza G, Brauer F, Neri I (2020) Modelling and simulating chikungunya spread with an unstructured triangular cellular automata. Infect Dis Model 5:197–220
Pandemic Influenza Outbreak Research Modelling Team (Pan-InfORM) (2009) Modelling an influenza pandemic: a guide for the perplexed. Can Med Assoc J 181(3–4): 171–173. https://doi.org/10.1503/cmaj.090885
Xiao D, Ruan S (1999) Bogdanov-Takens bifurcations in predator-prey systems with constant rate harvesting. Fields Inst Commun 21:493–506