Грекас Николаос
Применение преобразования Лапласа для эпидемиологических моделей в производных Капуто
Математическая биология и биоинформатика. 2024;19(1):61-76.
doi: 10.17537/2024.19.61.
Список литературы
- Minardi F. Fractional Calculus: Theory and Applications. Mathematics, 2018;6. Article No. 145. doi: 10.3390/math6090145
- Miller K. S., Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations. New York: Wiley, 1993.
- Abel N.H. Opløsning af et par opgaver ved hjelp af bestemte integraler. Magazin for Naturvidenskaberne. 1823;I(2):55-68 (in Danish).
- Caputo M. Linear Models of Dissipation whose Q is almost Frequency Independent—II. Geophysical Journal International. 1967;13(5):529-539. doi: 10.1111/j.1365-246X.1967.tb02303.x
- Sene N. Numerical methods applied to a class of SEIR epidemic models described by the Caputo derivative. In: Methods of Mathematical Modeling. Infectious Diseases. Eds. H. Singh, H. M. Srivastava, D. Baleanu. Academic Press, 2022. P. 23–40. doi: 10.1016/B978-0-323-99888-8.00003-6
- Caputo M., Fabrizio M. On the notion of fractional derivative and applications to the hysteresis phenomena. Meccanica. 2017;52:3043–3052. doi: 10.1007/s11012-017-0652-y
- Rezapour S., Mohammadi H., Jajarmi A. A New Mathematical Model for Zika Virus Transmission. Advances in Difference Equations. 2020. Article No. 589. doi: 10.1186/s13662-020-03044-7
- Debbouche N., Ouannas A., Batiha I. M., Grassi G. Chaotic dynamics in a novel COVID-19 pandemic model described by commensurate and incommensurate fractional-order derivatives. Nonlinear Dynamics. 2022;109:33–45. doi: 10.1007/s11071-021-06867-5
- Abbes A. Ouannas A., Shawagfeh N., Jahanshahi H. The fractional-order discrete COVID-19 pandemic model: stability and chaos. Nonlinear Dynamics. 2023;111:965-983. doi: 10.1007/s11071-022-07766-z
- Tunç O., Tunç C. Solution estimates to Caputo proportional fractional derivative delay integro-differential equations. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 2023;117. Article No. 12. doi: 10.1007/s13398-022-01345-y
- Hethcote H.W. Three Basic Epidemiological Models. In: Applied Mathematical Ecology. Ed. Levin S.A., Hallam T.G., Gross L.J. Berlin: Springer, 1989. (Biomathematics Series, V. 18). doi: 10.1007/978-3-642-61317-3_5
- Ross R. An application of the theory of probabilities to the study of a priori pathometry. Part I. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 1916;92(638):204–230. doi: 10.1098/rspa.1916.0007
- Ross R., Hudson H. An application of the theory of probabilities to the study of a priori pathometry. Part II. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 1917;93(650):212–225. doi: 10.1098/rspa.1917.0014
- Ross R., Hudson H. An application of the theory of probabilities to the study of a priori pathometry. Part III. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 1917;89(621):225–240. doi: 10.1098/rspa.1917.0015
- Kermack W.O., McKendrick A.G. A Contribution to the Mathematical Theory of Epidemics. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character. 1927;115(772):700–721. doi: 10.1098/rspa.1927.0118
- Kendall D.G. Deterministic and stochastic epidemics in closed populations. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability: Contributions to Biology and Problems of Health. 1956;4:149–165. doi: 10.1525/9780520350717-011
- Engelmann L. A box, a trough and marbles: How the Reed-Frost epidemic theory shaped epidemiological reasoning in the 20th century. History and Philosophy of the Life Sciences. 2021;43. Article No. 105. doi: 10.1007/s40656-021-00445-z
- Baleanu D., Aydogn S.E., Mohammadi H., Rezapour S. On modelling of epidemic childhood diseases with the Caputo-Fabrizio derivative by using the Laplace Adomian decomposition method. Alexandria Engineering Journal. 2020;59(5):3029-3039. doi: 10.1016/j.aej.2020.05.007
- Aghdaoui H., Tilioua M., Nissar K. S., Khan I. A Fractional Epidemic Model with Mittag-Leffler Kernel for COVID-19 Mathematical Biology and Bioinformatics. 2021;16(1):39-56. doi: 10.17537/2021.16.39
- Dablander F. Infectious diseases and nonlinear differential equations. 2020. https://fabiandablander.com/r/Nonlinear-Infection.html (accessed 22.03.2024).
- Dobrushkin V., Gourley R. The Laplace Transform. In: Brown University Applied Mathematis. 2016. https://www.cfm.brown.edu/people/dobrush/am33/MuPad/MuPad9.html (accessed 22.03.2024).
- Jarad F., Abdeljawad T. Generalized fractional derivatives and Laplace transform. Discrete and Continuous Dynamical Systems - S. 2020;13(3):709-722. doi: 10.3934/dcdss.2020039
- Samko S.G., Kilbas A.A., Marichev O.I. Fractional Integrals and Derivatives: Theory and Applications. Switzerland: Gordon and Breach, 1993.
- Luchko Y. Fractional Derivatives and the Fundamental Theorem of Fractional Calculus. Fractional Calculus and Applied Analysis. 2020;23:939–966. doi: 10.1515/fca-2020-0049
|
|
|
