Modeling plant virus propagation with delays

Plants play a vital role in the everyday life of all organisms on earth. Sometimes, however, plants become infected with a virus. This can have a devastating effect on the ecosystem that depends on it. An insect–vector can cause the transmission of the virus from plant to plant. In this paper, a system of ordinary differential equations was first used to model the interaction between the insects and the plants. We found the equilibria of the model, and we analyzed the stability using the Reproductive number, derived by the next generation matrix. Afterwards, we introduced a delay to the model and a system of delay differential equations (DDE) was obtained. Analysis of the DDEs dynamics was performed including equilibria, stability, and bifurcations. Then, numerical solutions of the ODE and the DDE were compared and conclusions are given.