Dynamics of a delayed plant disease model with Beddington-DeAngelis disease transmission

Abstract

In the present research, we study a mathematical model for vector-borne plant disease with the plant resistance to disease and vector crowding effect and propose using Beddington-DeAngelis type disease transmission and incubation delay. Existence and stability of the equilibria have been studied using basic reproduction number (R0). The region of stability of the different equilibria is presented and the impact of important parameters has been discussed. The results obtained suggest that disease transmission depends on the plant resistance and incubation delay. The delay and resistance rate can stabilise the system and plant epidemic can be avoided increasing plant resistance and incubation period.

Keywords

• mathematical model
• disease resistance
• crowding effect
• incubation period
• basic reproduction number
• stability
• hopf bifurcation