Numerical analysis of fractional order Pine wilt disease model with bilinear incident rate

Volume 17, Issue 3, pp 420-428

Publication Date: 2017-08-07

http://dx.doi.org/10.22436/jmcs.017.03.07

Authors

Yongjin Li - Department of Mathematics, Sun Yat-sen University, Guangzhou, China.
Fazal Haq - Department of Mathematics, Hazara University Mansehra, Pakistan.
Kamal Shah - Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan.
Muhammad Shahzad - Department of Mathematics, Hazara University Mansehra, Pakistan.
Ghaus ur Rahman - Department of Mathematics and Statistics, University of Swat, Pakistan.

Abstract

This work is related to an analytical solution of a fractional order epidemic model for the spread of the Pine wilt disease with bilinear incident rate. To obtain an analytical solution of the system of nonlinear fractional differential equations for the considered model. Laplace Adomian decomposition method (LADM) will be used. Comparison of the results have been carried out between the proposed method and that of homotopy purturbation (HPM). Numerical results show that (LADM) is very efficient and accurate for solving fractional order Pine wilt disease model.

Keywords

Pine Wilt Disease, bilinear incident rate, fractional derivatives, Laplace-Adomian decomposition method, analytical solution.

References

[1] A. Abdelrazec, Adomian decomposition method: convergence analysis and numerical approximations, M.sc. Dissertation, McMaster University, Hamilton, Ontario, (2008).
[2] J. Biazar, Solution of the epidemic model by Adomian decomposition method, Appl. Math. Comput., 173 (2006), 1101– 1106.
[3] F. Haq, K. Shah, G. U. Rahman, M. Shahzad, Numerical analysis of fractional order model of HIV-1 infection of \(CD4^+\) T-cells, Comput. Methods Differ. Equ., 5 (2017), 1–11.
[4] F. Haq, K. Shah, G. U. Rahman, M. Shahzad, Numerical solution of fractional order smoking model via laplace Adomian decomposition method, Alexandria Eng. J., (2017), 18 pages.
[5] H. N. Hassan, M. A. El-Tawil, A new technique of using homotopy analysis method for solving high-order nonlinear differential equations, Math. Methods Appl. Sci., 34 (2011), 728–742.
[6] K. S. Lee, D. Kim, Global dynamics of a Pine wilt disease transmission model with nonlinear incidence rates, Appl. Math. Model., 37 (2013), 4561–4569.
[7] K. S. Lee, A. A. Lashari, Global stability of a host-vector model for Pine wilt disease with nonlinear incidence rate, Abstr. Appl. Anal., 2014 (2014), 11 pages.
[8] S.-J. Liao, Beyond perturbation, Introduction to the homotopy analysis method, CRC Series: Modern Mechanics and Mathematics, Chapman & Hall/CRC, Boca Raton, FL, (2003).
[9] M. M. Mota, H. Braasch, M. A. Bravo, A. C. Penas, W. Burgermeister, K. Metge, E. Sousa, First report of Bursaphelenchus xylophilus in Portugal and in Europe, Nematology, 1 (1999), 727–734.
[10] A. Naghipour, J. Manafian, Application of the Laplace Adomian decomposition and implicit methods for solving Burgers’ equation, TWMS J. Pure Appl. Math., 6 (2015), 68–77.
[11] K. Shah, H. Khalil, R. A. Khan, Analytical solutions of fractional order diffusion equations by natural transform method, Iran. J. Sci. Technol. Trans. A Sci., 2016 (2016), 14 pages.
[12] X.-Y. Shi, G.-H. Song, Analysis of the mathematical model for the spread of Pine wilt disease, J. Appl. Math., 2013 (2013), 10 pages.
[13] F. Takasu, Individual-based modeling of the spread of Pine wilt disease: vector beetle dispersal and the Allee effect, Popul. Ecol., 51 (2009), 399–409.
[14] B. G. Zhao, K. Futai, R. Jack, J. R. Sutherland, Y. Takeuchi, Pine wilt disease, Springer, New York, (2008).

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