A Simple Linearization Procedure For Obtaining R-0 From Invasive Epidemic Models

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.