EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 17 (2022) Math. Model. Nat. Phenom., 17 (2022) 17 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 17, 2022
Article Number 17
Number of page(s) 31
DOI https://doi.org/10.1051/mmnp/2022021
Published online 17 June 2022
  1. M. Adimy, A. Chekroun and C.P. Ferreira, Global dynamics of a differential-difference system: a case of Kermack-McKendrick SIR model with age-structured protection phase. Math. Biosci. Eng. 17 (2020) 1329–1354. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Adimy, A. Chekroun and B. Kazmierczak, Traveling waves in a coupled reaction-diffusion and difference model of hematopoiesis. J. Differ. Equ. 262 (2017) 4085–4128. [CrossRef] [Google Scholar]
  3. M. Adimy, A. Chekroun and T. Kuniya, Traveling waves of a differential-difference diffusive Kermack-McKendrick epidemic model with age-structured protection phase. J. Math. Anal. Appl. 505 (2022) 125464. [CrossRef] [Google Scholar]
  4. M. Adimy, A. Chekroun and T.-M. Touaoula, Age-structured and delay differential-difference model of hematopoietic stem cell dynamics. Discr. Continu. Dyn. Syst. Ser. B 20 (2015) 2765–2791. [CrossRef] [Google Scholar]
  5. D.G. Aronson and H.F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics. Adv. Math. 30 (1978) 33–76. [CrossRef] [MathSciNet] [Google Scholar]
  6. H. Berestycki, G. Nadin, B. Perthame and L. Ryzhik, The non-local Fisher-KPP equation: travelling waves and steady states. Nonlinearity 22 (2009) 2813–2844. [CrossRef] [MathSciNet] [Google Scholar]
  7. G. Bocharov and K. Hadeler, Structured population models, conservation laws, and delay equations. J. Differ. Equ. 168 (2000) 212–237. [CrossRef] [Google Scholar]
  8. O. Bonnefon, J. Garnier, F. Hamel and L. Roques, Inside dynamics of delayed traveling waves. MMNP 8 (2013) 42–59. [CrossRef] [EDP Sciences] [PubMed] [Google Scholar]
  9. E. Bouin, V. Calvez and G. Nadin, Propagation in a kinetic reaction-transport equation: travelling waves and accelerating fronts. Arch. Ratl. Mech. Anal. 217 (2015) 571–617. [CrossRef] [Google Scholar]
  10. K.J. Brown and J. Carr, Deterministic epidemic waves of critical velocity. Math. Proc. Cambridge Philos. Soc. 81 (1977) 431–433. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. Chekroun, Existence and asymptotics of traveling wave fronts for a coupled nonlocal diffusion and difference system with delay. Electr. J. Qual. Theory Differ. Equ. 85 (2019) 1–23. [Google Scholar]
  12. J. Fang and X.-Q. Zhao, Existence and uniqueness of traveling waves for non-monotone integral equations with applications. J. Differ. Equ. 248 (2010) 2199–2226. [CrossRef] [Google Scholar]
  13. R.A. Fisher, The wave of advance of advantageous genes. Ann. Eugenics 7 (1937) 353–369. [Google Scholar]
  14. C. Gomez, H. Prado and S. Trofimchuk, Separation dichotomy and wavefronts for a nonlinear convolution equation. J. Math. Anal. Appl. 420 (2014) 1–19. [CrossRef] [MathSciNet] [Google Scholar]
  15. S.-A. Gourley and J. Wu, Delayed non-local diffusive systems in biological invasion and disease spread. Nonlinear Dyn. Evol. Equ. Am. Math. Soc. 48 (2006) 137–200. [Google Scholar]
  16. K.P. Hadeler, T. Hillen and M.A. Lewis, Biological Modeling with Quiescent Phases, in Spatial Ecology, edited by R.S. Cantrell, C. Cosner and S. Ruan. Mathematical and Computational Biology series, Chapman Hall/CRC Press (2009) 101–127. [Google Scholar]
  17. K.P. Hadeler and M.A. Lewis, Spatial dynamics of the diffusive logistic equation ith a sedentary compartment. Can. Appl. Math. Quart. 10 (2002) 473–499. [Google Scholar]
  18. F. Hamel and N. Nadirashvili, Travelling fronts and entire solutions of the Fisher-KPP equation in Rn. Arch. Ratl. Mech. Anal. 157 (2001) 91–163. [CrossRef] [Google Scholar]
  19. R. Huang, Stability of travelling fronts of the Fisher-KPP equation in Rn. Nonlinear Differ. Equ. Appl. 15 (2008) 599–622. [CrossRef] [Google Scholar]
  20. T. Kapitula, Multidimensional stability of planar travelling waves. Trans. Am. Math. Soc. 349 (1997) 257–269. [CrossRef] [Google Scholar]
  21. A. Kolmogorov, I. Petrovskii and N. Piskunov, Study of a diffusion equation that is related to the growth of a quality of matter, and its application to a biological problem. Byul. Mosk. Gos. Univ. Ser. A, Mat. Mekh. 1 (1937) 1–26. [Google Scholar]
  22. W. Li, S. Ruan and Z. Wang, On the diffusive Nicholson’s blowflies equation with nonlocal delay. J. Nonlinear Sci. 17 (2007) 505–525. [CrossRef] [MathSciNet] [Google Scholar]
  23. X. Liang and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications. Commun. Pure Appl. Math. 60 (2007) 1–40. [CrossRef] [Google Scholar]
  24. Z. Ling and Z. Lin, Traveling wavefront in a hematopoiesis model with time delay. Appl. Math. Lett. 23 (2010) 426–431. [CrossRef] [MathSciNet] [Google Scholar]
  25. M.C. Mackey, Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis. Blood 51 (1978) 941–956. [PubMed] [Google Scholar]
  26. J.D. Murray, Mathematical Biology: I. An Introduction. Springer, New York, 3rd edition (2002). [Google Scholar]
  27. D.H. Sattinger, On the stability of waves of nonlinear parabolic systems. Adv. Math. 22 (1976) 312–355. [CrossRef] [Google Scholar]
  28. K.W. Schaaf, Asymptotic behavior and traveling wave solutions for parabolic functional-differential equations. Trans. Am. Math. Soc. 302 (1987) 587–615. [Google Scholar]
  29. K. Schumacher, Travelling-front solutions for integro-differential equations. I. J. Reine Angew. Math. 316 (1980) 54–70. [MathSciNet] [Google Scholar]
  30. J.W.-H. So, J. Wu and X. Zou, A reaction-diffusion model for a single species with age structure. I Travelling wavefronts on unbounded domains. Proc. R. Soc. Lond. A 457 (2001) 1841–1853. [CrossRef] [MathSciNet] [Google Scholar]
  31. H.R. Thieme and X.-Q. Zhao, Asymptotic speeds of spread and traveling waves for integral equations and delayed reactiondiffusion models. J. Differ. Equ. 195 (2003) 430–470. [CrossRef] [Google Scholar]
  32. A.I. Volpert, V.A. Volpert and V.A. Volpert, Traveling Wave Solutions of Parabolic System. American Mathematical Soc. (1994). [Google Scholar]
  33. Z. Wang, W. Li and S. Ruan, Traveling fronts in monostable equations with nonlocal delayed effects. J. Dyn. Differ. Equ. 20 (2008) 573–607. [CrossRef] [Google Scholar]
  34. Z. Wang, W. Li and S. Ruan, Existence and stability of traveling wave fronts in reaction advection diffusion equations with nonlocal delay. J. Differ. Equ. 238 (2007) 153–200. [CrossRef] [Google Scholar]
  35. G.F. Webb, Population Models Structured by Age, Size, and Spatial Position, Lecture Notes in Mathematics, 1936. Springer (2008) 1–49. [Google Scholar]
  36. D.V. Widder, Laplace Transform. Princeton University Press (1946). [Google Scholar]
  37. J. Wu, Theory and Applications of Partial Functional Differential Equations. Springer (1996). [CrossRef] [Google Scholar]
  38. J. Wu and X. Zou, Traveling wave fronts of reaction-diffusion systems with delay. J. Dyn. Differ. Equ. 13 (2001) 651–687. [CrossRef] [Google Scholar]
  39. J. Wu and X. Zou, Erratum to "Traveling wave fronts of reaction-diffusion systems with delay". [J. Dyn. Differ. Equ. 13 (2001)]. J. Dyn. Differ. Equ. 20 (2008) 531–533. [CrossRef] [Google Scholar]
  40. J. Xin, Front propagation in heterogeneous media. SIAM Rev. 42 (2000) 161–230. [CrossRef] [MathSciNet] [Google Scholar]
  41. X.-Q. Zhao and W. Wang, Fisher waves in an epidemic model. Discr. Continu. Dyn. Syst. Ser. B 4 (2004) 1117–1128. [Google Scholar]
  42. X.-Q. Zhao and D. Xiao, The asymptotic speed of spread and traveling waves for a vector disease model. J. Dyn. Diff. Equ. 18 (2006) 1001–1019. [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.