### Comparison of the differential transformation method and non standard finite difference scheme for solving plant disease mathematical model

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N. Anggriani, N. Istifadah, M. Hanifah, and A. Supriatna. A mathematical model of protectant and curative fungicide application and its stability analysis. IOP Conference Series: Earth and Environmental Science, 31(1):012014, 2016.

N. Anggriani, M. Ndii, D. Arumi, N. Istifadah, and A. K. Supriatna. Mathematical model for plant disease dynamics with curative and preventive treatments. AIP Conference Proceeding, Accepted.

R. Anguelov and J. M.-S. Lubuma. Contributions to the mathematics of the nonstandard finite difference method and applications. Numerical Methods for Partial Differential Equations, 17(5):518–543, 2001.

A. J. Arenas, G. Gonzales-Parra, and B. M. Chen-Charpentier. Dynamical analysis of the transmission of seasonal disease using the differential transformation method. Mathematical and Computer Modelling, 50:765–776, 2009.

J. H. Arias, J. Gmez-Gardees, S. Meloni, and E. Estrada. Epidemics on plants: Modeling long-range dispersal on spatially embedded networks. Journal of Theoretical Biology, 453:1 – 13, 2018.

J. C. Butcher. The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods. John Wiley & Sons Inc, Jan. 1987.

M.-S. Chan and M. J. Jeger. An analytical model of plant virus disease dynamics with roguing and replanting. Journal of Applied Ecology, 31(3):413–427, 1994.

C.-L. Chen, L. Sy-Hong, and C.-K. Chen. Application of taylor transformation to nonlinear predictive control problem. Applied Mathematical Modelling, 20(9):699 – 710, 1996.

F. V. den Bosch and M. J. Jeger. The basic reproduction number of vector-borne plant virus epidemics. Virus Research, 241:196 – 202, 2017. Plant Virus Epidemiology.

O. Diekmann, H. Heesterbeek, and T. Britton. Mathematical Tools for Understanding Infectious Disease Dynamics. EBSCO ebook academic collection. Princeton University Press, 2013.

A. Gkdoan, M. Merdan, and A. Yildirim. Adaptive multi-step differential transformation method to solving nonlinear differential equations. Mathematical and Computer Modelling, 55(3):761 – 769, 2012.

I. A.-H. Hassan. Application to differential transformation method for solving systems of differential equations. Applied Mathematical Modelling, 32(12):2552 – 2559, 2008.

L. jun Xie, C. lian Zhou, and S. Xu. A new algorithm based on differential transform method for solving multi-point boundary value problems. International Journal of Computer Mathematics, 93(6):981–994, 2016.

T. A. McLennan-Smith and G. N. Mercer. Complex behaviour in a dengue model with a seasonally varying vector population. Mathematical Biosciences, 248:22 – 30, 2014.

R. E. Mickens. Nonstandard finite difference models of differential equations. world scientific, 1994.

R. E. Mickens. Applications of nonstandard finite difference schemes. World Scientific, 2000.

R. E. Mickens. Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition. Numerical Methods for Partial Differential Equations, 23(3):672–691, 2006.

R. E. Mickens. Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition. Numerical Methods for Partial Differential Equations, 23(3):672–691, 2007.

R. E. Mickens. Nonstandard Finite Difference Methods, pages 1–9. World Scientific, 2012.

P. K. Mondal and T. K. Kar. Optimal treatment control and bifurcation analysis of a tuberculosis model with effect of multiple re-infections. International Journal of Dynamics and Control, 5(2):367–380, 2017.

M. Z. Ndii, D. Allingham, R. Hickson, and K. Glass. The effect of Wolbachia on dengue outbreaks when dengue is repeatedly introduced. Theoretical Population Biology, 111:9 – 15, 2016.

M. Z. Ndii, D. Allingham, R. I. Hickson, and K. Glass. The effect of Wolbachia on dengue dynamics in the presence of two serotypes of dengue: symmetric and asymmetric epidemiological characteristics. Epidemiology and Infection, 144(13):2874–2882, 2016.

M. Z. Ndii, N. Anggriani, and A. K. Supriatna. Application of differential transformation method for solving dengue transmission mathematical model. Symposium on Biomathematics. AIP Conference Proceeding, 2018.

M. Z. Ndii and A. Supriatna. Stochastic mathematical models in epidemiology. Information, 20:6185–6196, 2017.

M. Nourifar, A. A. Sani, and A. Keyhani. Efficient multi-step differential transform method: Theory and its application to nonlinear oscillators. Communication in Nonlinear Science Numerical Simulation, 53:154–183, 2017.

Z. M. Odibat, C. Bertelle, M. Aziz-Alaoui, and G. H. Duchamp. A multi-step differential transform method and application to non-chaotic or chaotic systems. Computers and Mathematics with Applications, 59(4):1462–1472, 2010.

P. Raja Sekhara Rao, K. Venkata Ratnam, and M. Sita Rama Murthy. Stability preserving non standard finite difference schemes for certain biological models. International Journal of Dynamics and Control, 2018.

M. Rezaiee-Pajand and M. Hashemian. Modified differential transformation method for solving nonlinear dynamic problems. Applied Mathematical Modelling, 47:76 – 95, 2017.

M. Roberts, V. Andreasen, A. Lloyd, and L. Pellis. Nine challenges for deterministic epidemic models. Epidemics, 10:49 – 53, 2015.

L. Shampine and M. Reichelt. The matlab ode suite. SIAM Journal on Scientific Computing, 18(1):1–22, 1997.

A. Suryanto, W. M. Kusumawinahyu, I. Darti, and I. Yanti. Dynamically consistent discrete epidemic model with modified saturated incidence rate. Computational and Applied Mathematics, 32:373383, 2013.

D. Tambaru, B. S. Djahi, and M. Z. Ndii. The effects of hard water consumption on kidney function: Insights from mathematical modelling. AIP Conference Proceedings, 1937(1):020020, 2018.

E. Venturino, P. K. Roy, F. Al Basir, and A. Datta. A model for the control of the mosaic virus disease in jatropha curcas plantations. Energy, Ecology and Environment, 1(6):360–369, Dec 2016.

J. K. Zhou. Differential Transformation and Its Applications for Electrical Circuits. Huazhong University Press, Wuhan, China (in Chinese), 1986.

DOI: http://dx.doi.org/10.5614%2Fcbms.2018.1.2.4

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