Mathematical Treatment of Nonlinear Pine Wilt Disease Model: An Evolutionary Approach

Abstract

In human life, the forest plays an important role in safeguard-ing trees against disease infection. The pine wilt disease is one of the big threats for the forest and the environment. Optimum control the-ory is about discovering a complex system control rule over a period of time. In this paper Evolutionary Pade acute accent Approximation (EPA) scheme has been implemented for the treatment of non-linear pine wilt disease model. Evolutionary Pade acute accent Approximation scheme transforms the nonlinear pine wilt disease model into optimization problem. Initial conditions are con-verted into problem constraints and then constraint problem is converted into unconstraint problem by using penalty function. Sufficient parameter settings for EPA have been implemented. The simulations are numerical solutions of the model of pine wilt disease by solving the proven problem of optimization. It is also determined the threshold value for the fun-damental reproductive number and the endemic disease balance point of the model. Evolutionary Pade acute accent Approximation has provided convergence solution regarding relationship among the different population compart-ments for diseases equilibrium, it has been observed that the results EPA scheme are more reliable and significant when a comparison is drawn with Non-Standard Finite Difference (NSFD) numerical scheme. Finally, EPA scheme reduces the infected rates very fast. Further, in a strong contrast to NFSD, this technique has eliminated the need to provide step size.