Mathematical analysis of vector-borne diseases on plants

Abstract

Many models of vector borne infectious diseases have been constructed and analyzed mathematically. The host populations in such models are typically animals. This work deals with the specific case of a plant host population taking into consideration the particular properties of plants. The main epidemiological issues of transmission, persistency, thresholds, interventions, etc., are all considered in this setting and discussed on a representative set of two models - one epidemic and one endemic. The main properties of the models are formulated as theorems and illustrated via computer simulations. In particular, we provide some threshold parameters that summarize the dynamics of the system and help to choose appropriate and efficient control tools or strategies for crop protection. The full proofs of the theorems are omitted but their main ideas are discussed in some detail.