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 $\hslash$-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.

The goal of this paper is to utilize the homotopy perturbation method (HPM) and Laplace transform to provide an approximate analytical expression to the non-linear time-dependent reaction diffusion equation arising in a mathematical model of an immobilized enzyme system with external mass transfer resistance. This mathematical model is a non-steady, non-linear reaction diffusion equation based on Michaelis–Menten kinetics. Approximate analytical expressions are also provided for various geometries of the enzyme catalytic pellets, namely, planar, cylindrical, and spherical. Obtained semi-analytical expressions are proven to fit for all the parameters appearing in the system and for all the geometries of enzyme catalytic pellets. When comparing the numerical and approximate analytical solutions, satisfactory results are obtained. Also, approximate analytical expressions of the effectiveness factor (EF) of the immobilized system are presented, and the effect of parameters on the EF is also analyzed.