Huanglongbing (HLB, ex-greening) is the most devastating citrus disease around the world. We modelled HLB spread in scenarios with different populational levels of the main alternative host (Murraya paniculata) and Diaphorina citri Kuwayama, vector of HLB associated bacteria; and removal of HLB-symptomatic plants. A compartmental deterministic mathematical model was built for representing the HLB dynamics in the Reconcavo Baiano, Bahia State, Brazil. The model encompasses delays on latency and incubation disease periods and on the D. citri nymphal stages. The simulations indicated that the presence of alternative hosts at low proportion would not play a crucial role in HLB dynamics in situations of poor D. citri management, regardless of HLB-symptomatic plants eradication. Symptomatic citrus plants contribute more to increase the HLB-incidence than the alternative host in scenarios without a suitable D. citri management.
Plant diseases often cause yield losses in agriculture worldwide. In mathematical ecology, the concept of the basic (or basal) reproduction number, R 0 , has received little attention in the scientific literature related to phytopathogen transmission in plants. The spread and magnitude of outbreaks, the rate of invasion and infectivity of the etiologic agent, the contact complexities occurring among parasite and host, and its susceptibility and period of infectiousness are very important factors for epidemiological models. These mathematical models, when applied in ecology, can help to understand the spread of infections from phytopathogens (or pests) to plant hosts as well as detect potential risks of contamination or outbreaks by using the basic reproduction number in effective control strategies. In this study, the Maclaurin series concepts on the Force of Infection were applied to derive R 0 expressions from generic epidemiological SIR (Susceptible-Infected-Removed) models. Consequently, we were able to obtain these relations from three transmission-infection model examples. Then, once the expression of Force of Infection is known from the "infectious" problem studied, it is possible to apply this technique to formulate the R 0 relation and guide practicable strategies for dispersing invasive phytopathogen controls.
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