Open Access
| Issue |
Math. Model. Nat. Phenom.
Volume 20, 2025
|
|
|---|---|---|
| Article Number | 25 | |
| Number of page(s) | 34 | |
| Section | Fractional Dynamics in Natural Phenomena | |
| DOI | https://doi.org/10.1051/mmnp/2025025 | |
| Published online | 08 October 2025 | |
- O. Martin, Mathématiques et sciences sociales au XXème siècle. Rev. Hist. Sci. Hum. 6 (2002) 3–13. [Google Scholar]
- A. Rapoport, Spread of information through a population with socio-structural bias: I. Assumption of transitivity. Bull. Math. Biophys. 15 (1953) 523–533. [Google Scholar]
- F.M. Bass, A new product growth for model consumeR durables. Manag. Sci. 15 (1969) 215–227. [Google Scholar]
- L.M.A. Bettencourt, A. Cintrón-Arias, D.I. Kaiser and C. Castillo-Chávez, The power of a good idea: Quantitative modeling of the spread of ideas from epidemiological models. Physica A: Statist. Mech. Appl. 364 (2006) 513–536. [Google Scholar]
- J.S. Coleman, Introduction to Mathematical Sociology. Free Press of Glencoe, New York (1964) [Google Scholar]
- L. Bonnasse-Gahot, H. Berestycki, M.-A. Depuiset, M.B. Gordon, S. Roché, N. Rodriguez and J.-P. Nadal, Epidemiological modelling of the 2005 French riots: a spreading wave and the role of contagion. Sci. Rep. 8 (2018) 107. [Google Scholar]
- S.L. Burbeck, W.J. Raine and M.J.A. Stark, The dynamics of riot growth: an epidemiological approach. J. Math. Sociol. 6 (1978) 1–22. [Google Scholar]
- L.L. Cavalli-Sforza and M.W. Feldman, Cultural Transmission and Evolution: A Quantitative Approach. Princeton University Press (1981). [Google Scholar]
- B. Lahire, Les Structures Fondamentales Des Sociétés Humaines. La Decouverte (2023). [Google Scholar]
- R. Dawkins, The Selfish Gene, 2nd edn., vol. 2. Oxford University Press, USA (1990). [Google Scholar]
- W.O. Kermack and A.G. McKendrick, Contributions to the mathematical theory of epidemics—I. Bull. Math. Biol. 53 (1991) 33–55. [Google Scholar]
- R. Ducasse and S. Nordmann, Propagation properties in a multi-species SIR reaction-diffusion system. J. Math. Biol. 87 (2023) 16. [Google Scholar]
- O. Diekmann, Thresholds and travelling waves for the geographical spread of infection. J. Math. Biol. 6 (1978) 109130. [Google Scholar]
- R. Ducasse, Threshold phenomenon and traveling waves for heterogeneous integral equations and epidemic models. Nonlinear Anal. 218 (2022) Paper No. 112788, 34. [Google Scholar]
- A. Kallen, Thresholds and travelling waves in an epidemic model for rabies. Nonlinear Anal. Theory Methods Appl. 8 (1984) 851–856. [Google Scholar]
- A. Ducrot, Spreading speed for a KPP type reaction-diffusion system with heat losses and fast decaying initial data. J. Differ. Equ. 270 (2021) 217–247. [Google Scholar]
- 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. Moscow Univ. Math. Bull. 1 (1937) 1–26. [Google Scholar]
- D.G. Aronson and H.F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics. Adv. Math. 30 (1978) 33–76. [CrossRef] [MathSciNet] [Google Scholar]
- L.C. Evans, Partial Differential Equations, vol. 19 of Graduate Studies in Mathematics, 2nd edn. American Mathematical Society, Providence (Rhode Island) (2010). [Google Scholar]
- G.M. Lieberman, Second Order Parabolic Differential Equations. World Scientific (1996). [Google Scholar]
- D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, vol. 224 of Classics in Mathematics. Springer, Berlin, Heidelberg (2001). [Google Scholar]
- M.G. Krein and M.A. Rutman, Linear operators leaving invariant a cone in a Banach space. Uspekhi Mat. Nauk. 3 (1948) 3–95. [Google Scholar]
- H. Berestycki and L. Rossi, Generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains. Commun. Pure Appl. Math. 68 (2015 1014–1065. [Google Scholar]
- H. Berestycki and F. Hamel, Front propagation in periodic excitable media. Commun. Pure Appl. Math. 55 (2002) 949–1032. [Google Scholar]
- R. Ducasse and L. Rossi, Blocking and invasion for reaction-diffusion equations in periodic media. Calc. Var. Part. Differ. Equ. 57 (2018) 142. [Google Scholar]
- L. Rossi, The Freidlin-Gartner formula for general reaction terms. Adv. Math. 317 (2017) 267–298. [Google Scholar]
- F. Hamel, Formules min-max pour les vitesses d’ondes progressives multidimensionnelles. Ann. Fac. Sci. Toulouse: Math. 8 (1999) 259–280. [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.
