Modeling plant virus propagation with delays

Plants are essential for the survival of many species including man. Unfortunately there are many viruses that cause diseases to both crops and wild plants. In humans and animals, virus propagation can happen by direct contact or through a vector. But in plants, virus propagation can only happen through a vector, usually insects and in particular beetles. After biting an infected plant, the virus is transmitted to the vector. It takes some time for the virus to reproduce and infect the vector, who then can go and infect other plants. It also takes some time for the virus to propagate inside the newly infected plant. In this paper we present an epidemiological mathematical model assuming that both the plants and vectors have homogeneous populations. The model includes discrete time delays and is based on delay differential equations. Steady solutions, their stability and bifurcations are analyzed and numerical simulations are presented. keywords: delay differential equations, plant viruses, mathematical modeling [email protected] [email protected]