Exploring the impact of biocontrol and temperature variations on the population dynamics of Paracoccus marginatus

The mealybug (Paracoccus marginatus) is one of the most important pests of papaya (Carica papaya L.). The high potential damage of this pest threatens papaya production. The objective of this paper is to explore the impact of biocontrol and temperature variations on the population dynamics of Paracoccus marginatus (P. marginatus). We first propose and study a mathematical model for the dynamics of P. marginatus within a papaya field. This model consists of a time-delayed non-autonomous system of differential equations that takes into account the egg incubation period, temperature variations, plant compensation and predators that are natural enemies of the papaya pest. We provide the basic properties of the model, compute the basic offspring number N-0 and show that there exists two threshold parameters (N) under bar (0) and xi(0) such that (N) under bar (0) <= N-0 <= xi(0) <= 1 and N-0 >= (N) under bar (0) > 1 provide conditions for the extinction and persistence of the pest within the papaya field, respectively. After, we investigate the impact of biocontrol on the pest population. We found that the use of a control strategy based on constant releases of predators could reduce the pest population by 35.62 percent and increase the biomass by 77.50 percent, while the use of impulsive releases of predators result in a decrease of 96.31 percent of the pest population and an increases of 55.74 percent of the biomass. We also combine the use of continuous predator releases and bio-pesticides and discovered that a spray applied 90 days after germination could completely eliminate the pest population and boost the biomass by 81.58 percent.