Mathematical modeling and analysis of the effect of the rugose spiraling whitefly on coconut trees

Abstract

<abstract><p>Coconut trees are severely affected by the rugose spiraling whitefly (Aleurodicus rugioperculatus Martin), which is an exotic pest. The dynamics of the disease caused by this pest are analyzed using a mathematical model. The equilibrium points are proved to be locally and globally asymptotically stable under some conditions. Our study, with sensitivity analysis, reveals that the contact rate plays a crucial role in the system that has a direct impact on disease spread. Further, with optimal control, we evoke the optimum level of spraying insecticide, which results in better control over disease with minimum cost of spraying. Additionally, an approximate analytical solution has been derived using a homotopy analysis method. The $ \hbar $-curves are provided to validate the region of convergence. The analytical results are compared with the results of numerical simulation and they are found to be in good agreement. Our goal is to keep the spread under control so that yield is unaffected. Controlling the contact rate with control measures can reduce the risk of healthy trees becoming infected and the intensity of infection.</p></abstract>

Modelling of Irreversible Homogeneous Reaction on Finite Diffusion Layers

“…One of the toughest challenges, especially across a wide range of science and engineering applications, is solving nonlinear differential equations. Recently, the construction of an analytical solution has been the focus of numerous analytical techniques, such as the homotopy perturbation method (HPM) [14][15][16][17][18][19][20][21][22][23][24][25][26], the variational iteration method [27][28][29][30][31][32], the homotopy analysis method [33][34][35][36][37], the Akbari-Ganji method [38][39][40][41][42][43], the Taylor series method [44][45][46][47], and the differential transform method. Jalili et al [48][49][50] discussed the heat exchange in nanoparticles and solved the momentum and energy equation numerically.…”