Mathematical Modeling of Host-Parasitoid Dynamics for Sustainable Pest Management

Aims: The management of agricultural pest populations represents a critical challenge in sustainable crop production, particularly for challenging species like the tomato fruit borer, Helicoverpa armigera. The research work aimed in developing and analysing a novel mathematical model describing the interaction between the tomato fruit borer and its egg parasitoid, Trichogramma chilonis. The main objective of this study to analyze the stability of the proposed system of differential equations.

Model Formulation: The model incorporates stage-structured population dynamics and impulsive control measures, providing insights into biological pest control strategies. In this model the tomato borer is represented by the egg and larval stages, and the parasitoid is considered in terms of the parasitized eggs. This model assumes uniform spatial distribution of both host and parasitoid populations, constant environmental conditions affecting parameters like reproduction and mortality rates, and idealized parasitoid release conditions where the released amount p remains consistent across interventions.

Methodology: We used existing secondary data from research articles' instead of conducting primary field experiments for parameter identification for this mathematical model. The use of secondary data from peer-reviewed literature not only provides validated parameter values that have been rigorously tested and verified by multiple researchers, but also allows for the incorporation of findings from diverse geographical locations and climatic conditions.

Results: Stability analysis identified three equilibrium points: the trivial, host-only E0,coexistence equilibria E1, and E2. The coexistence equilibirium E2 found to be locally stable under optimal parasitoid release intervals and quantities. The equilibrium point E2= (9.14,0.02,5.71) represents a coexistence state in the host-parasitoid dynamics, where the tomato fruit borer's egg density stabilizes at 9.14, the density of parasitized eggs at 0.02, and the larval density stabilizes at 5.71. This equilibrium is analyzed through its associated eigenvalues. This stability provides a reliable basis for implementing successful biological pest control strategies in tomato cultivation, ensuring a resilient and sustainable ecosystem.