The global dynamics and optimal control of a plant epidemic model

Abstract

This paper proposes and investigates a model for the spread of an infection into a plant population, considering the effects of both primary and secondary infections. We determine the basic reproduction number of the plant pathogens R0 and prove that if R0 > 1, then the positive equilibrium is globally stable, provided that several auxiliary inequalities, determined using the geometric approach of Li and Muldowney [23], hold. Also, we find a necessary condition for the existence of optimal controls by applying Pontryagin’s Minimum Principle. Finally, a numerical example is given to illustrate the applicability of our analytical findings.