Stability and Hopf bifurcation analysis of a delayed eco-epidemiological model of IYSV disease dynamics in onion plants with nonlinear saturated incidence and logistic growth

Abstract

Iris Yellow Spot Disease (IYSD), caused by Iris Yellow Spot Virus (IYSV) is a destructive and fastspreading virus disease of onion plants worldwide. It is mainly transmitted by an insect vector called thrips tabaci in a persistent and propagative manner and as such, there is a significant latent time after acquisition of the virus by the vector and an incubation time is needed for the appearance of disease symptoms on plants. In this paper, we formulate and analyze a non-linear mathematical model to explore the dynamics of IYSV disease in onion plants using system of delay differential equations by incorporating incubation and latent periods as time delays factors. The delays are introduced by adding an exposed population for onion plants representing the plants that are infected but not yet infective and by taking into account that there is fraction of the newly exposed onion plants that do not die during incubation period before becoming infective. It is assumed that the onion plant grows logistically in the farm so that the total onion plant population is taken as variable. The local stability of the disease-free equilibrium in the presence of delays is investigated using Descartes’s rule of signs. We establish the sufficient conditions for the stability of the endemic equilibrium in presence of delays and we investigate the occurrence of Hopf bifurcation when certain conditions are satisfied by considering the two delays as bifurcation parameters. We compute the critical values of the delays which preserve the local asymptotic stability of the endemic equilibrium and the model shows an oscillatory behavior beyond these critical values. Finally, numerical simulations are performed and displayed graphically to support the analytical results, and the eco-epidemiological implications of the key outcomes are briefly discussed.