
AIMS Mathematics, 2020, 5(3): 18561880. doi: 10.3934/math.2020124
Research article Special Issues
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Fractional order SIR model with generalized incidence rate
1 Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa
2 Department of mathematics, City university of Science and Information Technology, Peshawar, KP, Pakistan
3 Department of mathematics university of Peshawar, KP, Pakistan
4 Department of mathematics Abdul Wali Khan university, Mardan, KP, Pakistan
Received: , Accepted: , Published:
Special Issues: Recent Advances in Fractional Calculus with Real World Applications
References
1. S. Ullah, M. A. Khan, J. F. GezAguilar, Mathematical formulation of hepatitis B virus with optimal control analysis, Optim. Contr. Appl. Meth., 40 (2019), 529544.
2. E. Bonyah, M. A. Khan, K. O. Okosun, et al. A theoretical model for Zika virus transmission, PLoS ONE, 12 (2017), 126.
3. S. Ullah, M. A. Khan, M. Farooq, et al. Modeling and analysis of Tuberculosis (TB) in Khyber Pakhtunkhwa, Pakistan, Math. Comput. Simulat., 165 (2019), 181199.
4. D. P. Ahokpossi, A. Atangana and D. P. Vermeulen, Modelling groundwater fractal flow with fractional differentiation via Mittag effler law, Eur. Phy. J. Plus, 132 (2017), 165.
5. M. A. Khan, Y. Khan and S. Islam, Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment, Phy. A., 493 (2018), 210227.
6. M. Caputo and M. Fabricio, A New Definition of Fractional Derivative without Singular Kernel, Progr. Fract. Differ. Appl., 1 (2015), 7385.
7. A. Atangana and D. Baleanu, New Fractional Derivatives with Nonlocal and NonSingular Kernel: Theory and Application to Heat Transfer Model, Therm. Sci., 20 (2016), 763769.
8. M. A. Khan, S. Ullah, M. Farhan, The dynamics of Zika virus with Caputo fractional derivative, AIMS Math., 4 (2019), 134146.
9. S. Ullah, M. A. Khan, M. Farooq, A new fractional model for tuberculosis with relapse via AtanganaBaleanu derivative, Chaos, Solitons and Fractals, 116 (2018), 227238.
10. S. Qureshi, A. Yusuf, Modeling chickenpox disease with fractional derivatives: From caputo to atanganabaleanu, Chaos, Solitons and Fractals, 122 (2019), 111118.
11. S. Qureshi, E. Bonyah, A. A. Shaikh, Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data, Phy. A, 535 (2019), 122.
12. Z. Wang, Y. K. Xie, J. Lu, et al. Stability and bifurcation of a delayed generalized fractionalorder prey redator model with interspecific competition, Appl. Math. Comput., 347 (2019), 360369.
13. X. Wang, Z. Wang, X. Huang, et al. Dynamic Analysis of a Delayed FractionalOrder SIR Model with Saturated Incidence and Treatment Functions, Int. J. Bifurcat. Chaos, 28 (2018), 1850180.
14. X. Wang, Z. Wang, H. Shen, Dynamical analysis of a discretetime SIS epidemic model on complex networks, Appl. Math. Lett., 94 (2019), 292299.
15. X. Wang, Z. Wang, J. Xia, Stability and bifurcation control of a delayed fractionalorder ecoepidemiological model with incommensurate orders, J. Franklin I., 356 (2019), 82788295.
16. M. A. Khan, K. Shah, Y. Khan, et al. Mathematical modeling approach to the transmission dynamics of pine wilt disease with saturated incidence rate, Int. J. Biomath., 11 (2018), 1850035.
17. F. Rao, P. S. Mandal and Y. Kang, Complicated endemics of an SIRS model with a generalized incidence under preventive vaccination and treatment controls, App. Math. Mod., 67 (2019), 3861.
18. M. A. Khan, M. Farhan, S. Islam, et al. Modeling the transmission dynamics of avian influenza with saturation and psychological effect, Discrete and Continuous Dynamical SystemsS, 12 (2019), 455474.
19. W. O. Kermack, A. G. MCKendrick, A contribution to the mathematical theory of epidemics, Proc. Roy. Soc. Lond. A, 115 (1927), 700721.
20. V. Capasso and G. Serio, A generalization of the KermackMckendrick deterministic epidemic model, Math. Biosci., 42 (1978), 4161.
21. A. Korobeinikov and P. K Maini, A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence, Math. Biosci. Eng., 1 (2004), 5760.
22. I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, Elsevier, 1999.
23. S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives: theory and applications, 1993.
24. H. Delavari, D. Baleanu, J. Sadati, Stability analysis of Caputo fractionalorder nonlinear systems revisited, Nonlinear Dyn., 67 (2012), 24332439.
25. C. VargasDeLeon, Volterratype Lyapunov functions for fractional order epidemic systems, Commun. Nonlinear Sci. Numer. Simul., 24 (2015), 7585.
26. J. Li, Y. Yang, Y. Xiao, et al. A class of Lyapunov functions and the global stability of some epidemic models with nonlinear incidence, J. Appl. Anal. Comput., 6 (2016), 3846.
27. J. J. Wang, J. Z. Zhang and Z. Jin, Analysis of an SIR model with bilinear incidence rate, Nonlinear Analysis: Real World Applications, 11 (2010), 23902402.
28. M. A. Khan, Q. Badshah, S. Islam, et al. Global dynamics of SEIRS epidemic model with nonlinear generalized incidences and preventive vaccination, Adv. Diff. Equ., 2015 (2015), 88.
29. M. A. Khan, Y. Khan and S. Islam, Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment, Phy. A., 493 (2018), 210227.
30. X. Liu and L. Yang, Stability analysis of an SEIQV epidemic model with saturated incidence rate, Nonlinear Analysis: Real World Applications, 13 (2012), 26712679.
31. J. R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, The Journal of Animal Ecology, (1975), 331341.
32. D. L. DeAngelis, R. A. Goldstein and R. V. Oeill, A model for tropic interaction, Ecology, 56 (1975), 881892.
33. K. Hattaf, M. Mahrouf, J. Adnani, et al. Qualitative analysis of a stochastic epidemic model with specific functional response cand temporary immunity, Phys. A, 490 (2018), 591600.
34. Z. M. Odibat and N. T. Shawagfeh, Generalized taylor's formula, Appl. Math. Comput., 186 (2007), 286293.
35. W. Lin, Global existence theory and chaos control of fractional differential equations, J. Math. Anal. Appli., 332 (2007), 709726.
36. M. Toufik, A. Atangana, New numerical approximation of fractional derivative with nonlocal and nonsingular kernel: application to chaotic models, Eur. Phys. J. Plus, 132 (2017), 444.
© 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)