A four-compartment model of Diaphorina citri and Tamarixia radiata with citrus flushing dynamics and impulsive parasitoid releases

Diaphorina citri is the primary vector of Huanglongbing (HLB), a devastating disease that affects global citrus production. Effective biological control using the parasitoid Tamarixia radiata represents a sustainable alternative to chemical insecticides, but its efficacy depends heavily on environmental variables and resource availability. In this work, we develop a four-compartment mathematical model to analyze the dynamics of D. citri in the presence of T. radiata , a known parasitoid. Our model incorporates the cyclical and periodic behavior of citrus flushing (new shoots), providing a qualitative representation of resource-limited dynamics broadly consistent with field observations. Through comparative simulations of three scenarios, without parasitoid, a single initial introduction, and periodic augmentative releases, we characterize and compare the impact of T. radiata as a biological control agent. Our results show that periodic releases maintain pest suppression, whereas a single introduction produces a substantial but incomplete reduction in pest pressure that persists without fully dissipating over the simulated horizon. A sensitivity analysis over the release period and magnitude, together with an invasion-exponent stability criterion, delineates the region of the release-schedule parameter space predicted to achieve eradication rather than mere suppression. Additional checks confirm that this suppression is robust to imperfect release synchrony and quantify the conditions under which the model’s boundedness and mass-action assumptions hold. By aligning theoretical modeling with ecological reality, this framework supports the role of T. radiata in pest suppression and provides a baseline for future work on optimal and cost-effective release strategies. We frame this model explicitly as a qualitative first-approximation theoretical tool rather than a field-validated predictive one, given the absence of empirical calibration and independent validation against laboratory or empirical data. Within this scope, the predicted suppression of D. citri density is best read as a proxy for reduced HLB transmission risk, since vector control remains the standard management strategy for the disease in the absence of a direct treatment for the causal bacterium.