On application of differential transformation method to solve host-vector-predator system

The mathematical model has been used to understand many phenomena and natural interactions. Since including many variables and parameters, the complex models are not easy to find analytical solutions. The Differential Transformation Method (DTM) is an alternative numerical method used to solve a system of differential equations. In this paper, we develop the DTM for the Host-Vector-Predator model. The models consist of systems of differential equations describing the plant disease spread taking into account the biological agent as a predator for the vector. To illustrate the capability of the methods, some simulations with different parameters have been constructed. Numerical comparison showed good agreement with Runge-Kutta Method. These results show that the technique introduced here is accurate and easy to apply.

[1]  L. Madden,et al.  Plant Virus Epidemiology: Applications and Prospects for Mathematical Modeling and Analysis to Improve Understanding and Disease Control. , 2017, Plant disease.

[2]  Mathematical modeling approach to the transmission dynamics of pine wilt disease with saturated incidence rate , 2018 .

[3]  B. Soltanalizadeh.  Differential transformation method for solving one-space-dimensional telegraph equation , 2011 .

[4]  C. Bervillier,et al.  Status of the differential transformation method , 2011, Appl. Math. Comput..

[5]  Population biology and epidemiology of plant virus epidemics: from tripartite to tritrophic interactions , 2012, European Journal of Plant Pathology.

[6]  Asep K. Supriatna,et al.  Comparison of the differential transformation method and non standard finite difference scheme for solving plant disease mathematical model , 2018, Communication in Biomathematical Sciences.

[7]  L. Allen,et al.  Optimal control of a vectored plant disease model for a crop with continuous replanting , 2019, Journal of biological dynamics.

[8]  T. Onyango,et al.  Mathematical Analysis of Plant Disease Dispersion Model that Incorporates wind Strength and Insect Vector at Equilibrium , 2017 .

[9]  Asep K. Supriatna,et al.  The optimal control of rice tungro disease with insecticide and biological agent , 2020 .

[10]  Asep K. Supriatna,et al.  Optimal control issues in plant disease with host demographic factor and botanical fungicides , 2018 .

[11]  F. C. van den Bosch,et al.  Interactions in a host plant-virus-vector-parasitoid system: modelling the consequences for virus transmission and disease dynamics. , 2011, Virus research.

[12]  Farshid Mirzaee.  Differential Transform Method for Solving Linear and Nonlinear Systems of Ordinary Differential Equations , 2011 .

[13]  Jafar Biazar,et al.  Analytic solution for Telegraph equation by differential transform method , 2010 .

[14]  Matematik,et al.  Numerical Methods for Ordinary Differential Equations: Butcher/Numerical Methods , 2005 .

[15]  Christopher A Gilligan,et al.  Estimating epidemiological parameters from experiments in vector access to host plants, the method of matching gradients , 2020, PLoS Comput. Biol..

[16]  Asep K. Supriatna,et al.  Application of differential transformation method for solving dengue transmission mathematical model , 2018 .

[17]  H. A. Hosham,et al.  Mathematical Model of Vector-Borne Plant Disease with Memory on the Host and the Vector , 2016 .