Abstract
Viruses infect humans and animals but also infect plants and cause great economic and ecological damage. In most cases, the virus is transmitted by a vector. After being bitten by an infected vector, the virus takes some time to replicate and spread in the plant. We present two models of the spread of viruses in plants based on ordinary differential equations, and then add either a delay or an exposed plant population. We study two ways of adding the delay. In the first one, a plant infected by a vector changes from susceptible to infective after a time equal to the delay. In the second one, immediately after the contact between a susceptible plant and infective vector, the plant is no longer susceptible, but it takes time equal to the delay for it to turn infective. To better explain the two ways of incorporating the delays, we first introduce them in a simple SIRS model. We analyze the models and study their stability numerically. We conclude by studying the interactions and the conservation of the total plant population that the first way of introducing the delay is better justified.
Highlights
Plants are fundamental members of all ecosystems and their health is of the utmost importance to man and animals
The main objective of this paper is to study the different ways of incorporating the infection times and comparing the solutions and their stability for the different alternatives
We present the results for Model A with a constant plant population and Model B with a non-constant plant population
Summary
Plants are fundamental members of all ecosystems and their health is of the utmost importance to man and animals. Viruses may be transmitted from plant by plant by different mechanisms that can be either mechanical such as by agricultural tools or biological mainly by vectors such as insects but there is sometimes vertical transmission [2]. The vectors consume sap from an infected plant and the viruses circulate within the vector but do not replicate, do not cause the vector to become ill, and the vector will hold the virus for the rest of its life. Once inside the plant the virus propagates and the plant may use defense mechanisms to combat the virus. It may use antiviral RNA silencing [8]
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