The Dynamics of an Age-structured Pest Management Model

This paper investigates a compartmental pest management model which divides the pest population into a susceptible and an infective class, while also including a class of pathogenic viruses. The model is age-structured, in the sense that it accounts for the differences in the amounts of pathogenic viruses released by infective pests at various infection ages. First, the asymptotic behavior of the system is established via a monotonicity analysis which makes use of several integral inequalities. The linearized stability of the equilibria for the system is then discussed by means of Michailov criterion. As an outcome of our analysis, it is observed that the maximal length of the infective period plays an important role in the dynamics of the system. Several pest control strategies are further investigated by means of numerical simulations, the paper being concluded with a discussion on the biological significance of the mathematical findings.