RUS  ENG
Полная версия
ЖУРНАЛЫ // Математическая биология и биоинформатика

Матем. биология и биоинформ., 2021, том 16, выпуск 1, страницы 39–56 (Mi mbb457)

A fractional epidemic model with Mittag-Leffler kernel for COVID-19
Hassan Aghdaoui, Mouhcine Tilioua, Kottakkaran Sooppy Nisar, Ilyas Khan

СПИСОК ЛИТЕРАТУРЫ

1. Atangana A., Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?, Chaos, Solitons & Fractals, 136 (2020), 109860  crossref  mathscinet  scopus
2. Atangana A., Araz S.I., “Mathematical model of COVID-19 spread in Turkey and South Africa: Theory, methods and applications”, Advances in Difference Equations, 2020:1 (2020), 1–89  crossref  mathscinet
3. Yang Y., Lu Q., Liu M., Wang Y., Zhang A., Jalali N., Dean N.E., Longini I., Halloran M.E., Xu B., et al., Epidemiological and clinical features of the 2019 novel coronavirus outbreak in China, medRxiv, 2020, 89 pp.  crossref  mathscinet
4. Diekmann O., Heesterbeek J.A.P., Metz J.A.J., “On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations”, Journal of Mathematical Biology, 28:4 (1990), 365–382  crossref  mathscinet  zmath  scopus
5. World Health Organization Website, https://www.who.int/ (accessed 29.04.2021)
6. Atangana A., Alkahtani B.S., “Analysis of the Keller-Segel model with a fractional derivative without singular kernel”, Entropy, 17:6 (2015), 4439–4453  crossref  mathscinet  zmath  adsnasa  scopus
7. Atangana A., Baleanu D., “New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model”, Thermal Science, 20 (2016), 763–769  crossref  scopus
8. Atangana A., Koca I., “On the new fractional derivative and application to nonlinear Baggs and Freedman model”, J. Nonlinear Sci. Appl., 9:5 (2016), 2467–2480  crossref  mathscinet  zmath  scopus
9. Yavuz M., Özdemir N., Baskonus H.M., “Solutions of partial differential equations using the fractional operator involving Mittag-Leffler kernel”, The European Physical Journal Plus, 133:6 (2018), 1–11  crossref  adsnasa  scopus
10. Saad K.M., Deniz S., Baleanu D., “On a new modified fractional analysis of Nagumo equation”, International Journal of Biomathematics, 12:03 (2019), 1950034  crossref  mathscinet  zmath  scopus
11. Yusuf A., Qureshi S., Inc M., Aliyu A.I., Baleanu B., Shaikh A.A., “Two-strain epidemic model involving fractional derivative with Mittag-Leffler kernel”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 28:12 (2018), 123121  crossref  mathscinet  zmath  scopus
12. Bildik N., Deniz S., “A new fractional analysis on the polluted lakes system”, Chaos, Solitons & Fractals, 122 (2019), 17–24  crossref  mathscinet  zmath  adsnasa  scopus
13. Uçar S., “Existence and uniqueness results for a smoking model with determination and education in the frame of non-singular derivatives”, Discrete Contin. Dyn. Syst. Ser. A, 2018, 1–17  crossref  mathscinet  scopus
14. Hethcote H., “The mathematics of infectious diseases”, SIAM Review, 42:4 (2000), 599–653  crossref  mathscinet  zmath  adsnasa  scopus
15. Brauer F., “Mathematical epidemiology: Past, present, and future”, Infectious Disease Modelling, 2:2 (2017), 113–127  crossref  scopus
16. Yang C., Wang J., “A mathematical model for the novel coronavirus epidemic in Wuhan, China”, Mathematical Biosciences and Engineering, 17:3 (2020), 2708  crossref  mathscinet  zmath  scopus
17. Khan M.A., Ullah S., Farooq M., “A new fractional model for tuberculosis with relapse via Atangana-Baleanu derivative”, Chaos, Solitons & Fractals, 116 (2018), 227–238  crossref  mathscinet  zmath  adsnasa  scopus
18. Khan M.A., Atangana A., “Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative”, Alexandria Engineering Journal, 59:4 (2020), 2379–2389  crossref  scopus
19. Ullah M.Z., Alzahrani A.K., Baleanu D., “An efficient numerical technique for a new fractional tuberculosis model with nonsingular derivative operator”, Journal of Taibah University for Science, 13:1 (2019), 1147–1157  crossref
20. Khan M.A., Atangana A., “Dynamics of Ebola Disease in the Framework of Different Fractional Derivatives”, Entropy, 21:3 (2019), 303  crossref  mathscinet  scopus
21. Khan M.A., Ismail M., Ullah S., Farhan M., “Fractional order SIR model with generalized incidence rate”, AIMS Mathematics, 5:3 (2020), 1856–1880  crossref  mathscinet  scopus
22. The Moroccan Ministry of Public Health, COVID-19 Platform, http://www.covidmaroc.ma/Pages/AccueilAR.aspx (accessed 29.04.2021)
23. Shaikh A.S., Shaikh I.N., Nisar K.S., “A Mathematical Model of COVID-19 Using Fractional Derivative: Outbreak in India with Dynamics of Transmission and Control”, Advances in Difference Equations, 2020:1 (2020), 1–19  crossref  mathscinet  zmath
24. Shaikh A.S., Jadhav V.S., Timol M.G., Nisar K.S., Khan I., Analysis of the COVID-19 Pandemic Spreading in India by an Epidemiological Model and Fractional Differential Operator, Preprints, 2020, 16 pp.  crossref
25. 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 haracter, 115:772 (1927), 700–721  crossref  zmath  adsnasa
26. Prakasha D.G., Veeresha P., Baskonus H.M., “Analysis of the dynamics of hepatitis E virus using the Atangana-Baleanu fractional derivative”, The European Physical Journal Plus, 134:5 (2019), 1–11  crossref  scopus
27. Mekkaoui T., Atangana A., “New numerical approximation of fractional derivative with non-local and non-singular kernel: application to chaotic models”, The European Physical Journal Plus, 132:10 (2017), 1–16  crossref  mathscinet  scopus
28. Atangana A., Owolabi K.M., “New numerical approach for fractional differential equations”, Mathematical Modelling of Natural Phenomena, 13:1 (2018), 3  crossref  mathscinet  zmath  scopus
29. Rihan F.A., Al-Mdallal Q.M., AlSakaji H.J., Hashish A., “A fractional-order epidemic model with time-delay and nonlinear incidence rate”, Chaos, Solitons & Fractals, 126 (2019), 97–105  crossref  mathscinet  zmath  adsnasa  scopus
30. Ahmad S., Ullah A., Al-Mdallal Q.M., Khan H., Shah K., Khan A., “Fractional order mathematical modeling of COVID-19 transmission”, Chaos, Solitons & Fractals, 2020  crossref  mathscinet  scopus
31. Asif M., Khan Z.A., Haider N., Al-Mdallal Q., “Numerical simulation for solution of SEIR models by meshless and finite difference methods”, Chaos, Solitons & Fractals, 141 (2020), 110340  crossref  mathscinet  scopus
32. Asif M., Jan S.U., Haider N., Al-Mdallal Q., Abdeljawad T., “Numerical modeling of NPZ and SIR models with and without diffusion”, Results in Physics, 19 (2020), 103512  crossref  scopus
33. Hajji M.A., Al-Mdallal Q., “Numerical simulations of a delay model for immune system-tumor interaction”, Sultan Qaboos University Journal for Science, 23:1 (2018), 19–31  crossref
34. Thabet S.T.M., Abdo M.S., Shah K., Abdeljawad T., “Study of transmission dynamics of COVID-19 mathematical model under ABC fractional order derivative”, Results in Physics, 19 (2020), 103507  crossref  scopus


© МИАН, 2026