On a fractional order Ebola epidemic model

Advances in Difference Equations

Volumn 2015, Issue 1, 2015, Pages

  Area, Ivan ^a   Batarfi, Hanan ^b   Losada, Jorge ^c   Nieto, Juan J ^b,c   Shammakh, Wafa ^b   Torres, Ángela ^c  

^a UNIVERSITY OF VIGO   (Spain)

^b KING ABDULAZIZ UNIVERSITY   (Saudi Arabia)

^c UNIVERSITY OF SANTIAGO DE COMPOSTELA   (Spain)

Author keywords

Ebola; epidemiological model; fractional derivative

Indexed keywords

EID: 84941343624     PISSN: 16871839     EISSN: 16871847     Source Type: Journal    
DOI: 10.1186/s13662-015-0613-5     Document Type: Article

References (22)

1. Chua, KB, Crameri, G, Hyatt, A, Yu, M, Tompang, MR, et al.: A previously unknown reovirus of bat origin is associated with an acute respiratory disease in humans. Proc. Natl. Acad. Sci. 104, 11424-11429 (2007)
2. Gire, SK, Goba, A, Andersen, KG, Sealfon, RSG, Park, DJ, et al.: Genomic surveillance elucidates Ebola virus origin and transmission during the 2014 outbreak. Science 345, 1369-1372 (2014)
3. Chowell, G, Hengartner, N, Castillo-Chavez, C, Fenimore, P, Hyman, J: The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda. J. Theor. Biol. 229, 119-126 (2004)
4. WHO Ebola Response Team: Ebola virus disease in West Africa - the first 9 months of the epidemic and forward projections. N. Engl. J. Med. 371, 1481-1495 (2014)
5. Astacio, J, Briere, DM, Guillén, M, Martínez, J, Rodríguez, F, et al.: Mathematical models to study the outbreaks of Ebola. Technical report, MTBI Technical Report (1996) https://mtbi.asu.edu/research/archive/paper/mathematical-models-study-outbreaks-ebola
6. Lekone, PE, Finkenstädt, BF: Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study. Biometrics 62, 1170-1177 (2006)
7. Ndanguza, D, Tchuenche, JM, Haario, H: Statistical data analysis of the 1995 Ebola outbreak in the Democratic Republic of Congo. Afr. Math. 24, 55-68 (2013)
8. Althaus, CL: Estimating the reproduction number of Ebola virus (EBOV) during the 2014 outbreak in West Africa. Technical report, PLOS Current Outbreaks (2014)
9. Atangana, A, Doungmo Goufo, EF: On the mathematical analysis of Ebola hemorrhagic fever: deathly infection disease in West African countries. BioMed Research International (2014)
10. Gomes, MFC, Pastore y Piontti, A, Rossi, L, Chao, D, Longini, I, et al.: Assessing the international spreading risk associated with the 2014 West African Ebola outbreak. Technical report, PLOS Currents Outbreaks (2014)
11. Rivers, CM, Lofgren, ET, Marathe, M, Eubank, S, Lewis, BL: Modeling the impact of interventions on an epidemic of Ebola in Sierra Leone and Liberia. Technical report, PLOS Currents Outbreaks (2014)
12. Rachah, A, Torres, DFM: Mathematical modelling, simulation, and optimal control of the 2014 Ebola outbreak in West Africa. Discrete Dyn. Nat. Soc. 2015, Article ID 842792 (2015)
13. Anderson, R, May, R: Infectious Diseases of Humans: Dynamics and Control. Oxford Science Publications, Oxford (1992)
14. Li, C, Zeng, F, Liu, F: Spectral approximations to the fractional integral and derivative. Fract. Calc. Appl. Anal. 15, 383-406 (2012)
15. Al-Sulami, H, El-Shahed, M, Nieto, JJ, Shammakh, W: On fractional order dengue epidemic model. Math. Probl. Eng. (2014). doi:10.1155/2014/456537
16. Diethelm, K, Freed, AD: The FracPECE subroutine for the numerical solution of differential equations of fractional order (2002) http://www.mpg.de/billing/hbp98/diethelm.pdf
17. Du, M, Wang, Z, Hu, H: Measuring memory with the order of fractional derivative. Sci. Rep. 3, 3431 (2013)
18. Skwara, U, Martins, J, Ghaffari, P, Aguiar, M, Boto, J, Stollenwerk, N: Fractional calculus and superdiffusion in epidemiology: shift of critical thresholds. In: Proceedings of the 12th International Conference on Computational and Mathematical Methods in Science and Engineering, La Manga (2012)
19. Area, I, Djida, JD, Losada, J, Nieto, JJ: On fractional orthonormal polynomials of a discrete variable. Discrete Dyn. Nat. Soc. 2015, Article ID 141325 (2015)
20. Area, I, Losada, J, Manintchap, A: Fract. Calc. Appl. Anal. 18(5) (2015, to appear). doi:10.1515/fca-2015-0067; http://www.degruyter.com/view/j/fca
21. Kilbas, AA, Srivastava, HM, Trujillo, JJ: Theory and Applications of Fractional Differential Equations, xvi+523 p. North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam (2006)
22. Podlubny, I: Fractional Differential Equations. Mathematics in Science and Engineering, vol. 198. Academic Press, San Diego (1999)