Plants and age-structured pest dynamics with natural enemy as control strategy: A fractional differential equations model

Abstract

In recent years, plant pests have drawn much attention from researchers. Biological control proved an efficient replacement for chemical and other pest control techniques. The present study proposes the cognition of an immature pest population unaffected by the natural enemy and grows exponentially by the harvesting effort of the mature pest population to plants. The fractional calculus environment proposes A four-compartment: plant, immature and mature pest, and natural enemy model. Equilibrium points and the system’s stability are studied theoretically and numerically. Simulation study for different values of fractional order generates the optimum solution. The suggested method is much more benignant than the existing method of ordinary differential equations as we can figure out the infrequent changes in the variable using a fractional derivative. Creating the memory effect in the system using fractional derivatives makes it more realistic.

Keywords

• Fractional order derivative
• Four compartmental dynamical system
• Stability analysis
• Numerical simulations