Stability and bifurcation analysis of a multi-delay model for mosaic disease transmission

Abstract

A mathematical model is developed for analysis of the spread of mosaic disease in plants, which account for incubation period and latency that are represented by time delays. Feasibility and stability of different equilibria are studied analytically and numerically. Conditions that determine the type of behavior exhibited by the system are found in terms of various parameters. We have derived the basic reproduction number and identify the conditions resulting in eradication of the disease, as well as those that lead to the emergence of stable oscillations in the population of infected plants, as a result of Hopf bifurcation of the endemic equilibrium. Numerical simulations are performed to verify the analytical results and also to illustrate different dynamical regimes that can be observed in the system. In this research, the stabilizing role of both the time delay has been established i.e. when delay time is large, disease will persist if the infection rate is higher. The results obtained here are useful for plant disease management.

Keywords

• mathematical model
• time delay
• basic reproduction ratio
• transcritical and hopf bifurcation
• numerical stability and simulations