Mathematical Modeling of Host-Pest Interac-tions in Stage-Structured Populations: a Case of False Codling Moth [Thaumatotibia Leucotreta]

Abstract

Abstract false codling moth (FCM) (Thaumatotibia lucotreta) is a significant pest due to its potential eco-nomic impact on many susceptible fruits in most temperate regions of the world. Efforts to controlthe codling moth in the past mostly relied on the use of broad spectrum insecticide sprays, which hasresulted in the development of insecticide resistance, and the disruption of the control of secondarypests. Understanding the dynamic of this pest is of great in importance in order to effectively employthe most effective control strategies. In this study, a mathematical model of host-false codling mothinteractions is developed and qualitatively analysed using stability theory of system of differentialequations. The basic offspring number with respect to FCM free equilibrium is obtain using nextgeneration matrix. The condition for local and global asymptotic stability of FCM free and coexis-tence equilibria are established. The model is analysed numerically and graphically represented tojustify the analytical results.