Mathematical Modelling of Lesser Date Moth Using Sex Pheromone Traps and Natural Enemies

Abstract

In this paper, a mathematical model for lesser date moth is proposed and analyzed. The interaction between the date palm tree, lesser date moth, and natural enemy has been investigated. The impact of sex pheromone traps on lesser date moth is demonstrated. Some sufficient conditions are obtained to ensure the local and global stability of equilibrium points. The occurrence of local bifurcation near the equilibrium points is performed using Sotomayor’s theorem. Theoretical results are illustrated using numerical simulations.

Deterministic and Stochastic Fractional Order Model for Lesser Date Moth

“…Following [10][11][12][13][14], the model of lesser date moth with mating disruption and sex pheromone trap is describing by the following system…”

“…5 shows that the deterministic fractional-order remains stable for different values of fractional-order α though solutions reach to equilibrium point E 2 (7.5, 113.614, 111.386, 140.149, 189) more slowly for a smaller value of fractional-order α. It is important to notice that when α = 1 the fractional order model for lesser date moth (1) reduces to the classical integer-order model [10][11][12][13][14].…”