A compartmental model for vector transmitted diseases: an application to Xylella fastidiosa

In 2016 the presence of the bacterium Xylella fastidiosa was detected in Majorcan almond trees
and was regarded as the causal pathogen agent of the mortality of these trees over the last fifteen
years. Xylella fastidiosa, being endemic of the Americas, is an insect-transmitted bacterium which
is considered one of the major threats to plants worldwide for its large number of hosts, strains
and potential vectors. By 2017 the reported incidence of the bacterium over Majorcan almond
trees was 79.5% ± 2.0, presenting a great danger to one of the historical crops of the Balearic
Islands. then, the aim of this project is to develop a first step on the study of this epidemic by
means of a deterministic compartmental (mean-field) model. In particular, we present a model
for the vector assisted transmission of the pathogen, performing an analytical and computational
analysis. The model incorporates the specific biological and epidemiological considerations of the
bacterium Xylella fastidiosa and its interactions with insects and hosts in Majorca Island. In our
work the vector (insect) population varies with time, mimicking the field observations. One of the
conclusions is that, in general, this temporal variation hinders the theoretical characterization of
epidemic thresholds. We show that only in the case that the vector population is all the time in its
stationary value, the epidemic threshold can be calculated using the standard techniques, and we
numerically characterize the value of this threshold.