Libro de Resúmenes / Book of Abstracts (Español/English)

Resumenes 109
The mite show a preference to reproduce in drone cells, but soon
become overcrowded as the mite population increase. This leads to intermite
competition for limited food and space (the carrying capacity)
[5],[7],[8]. The drone cells available, in this work, are approximately 4% of
the worker cells.
A yearly function based in empiric data, which can be adapted to
different climatic regions, represent the brood bee cells available to the mite
invasion during the year.
This new model, like others of the same type [1] allow to study the
dynamic details as functions of the important biological parameters.
Otherwise, the model agree with the results in other models of Varroa
Destructor used before, like discrete model [2] [3] and continuous with lags
[6].
Finally, certain biological control strategy be evaluated as diminish
the number of available drone cells, by replacing comb cells, to decrease
the use of chemicals. This can be important for countries that produce and
exports bee’s honey, because they must be adapted to the rigid
international norms.
The system of differential equation for the growth of the mite
population is the following:
Referencias
dM
= γ 1D
+ γ 2W
− µ M
dt
dD
D
= r1φ
() t ( 1−
ς ( D ) M ( 1−
) − γ 1D
− µ 1D
dt
K
dW
dt
= r φ
2
() t ς ( D)
M − γ W − µ W.
In this work we take the preference function:
D
ς ( D)
= θ + ξ .
K1
θ + ξ = 1.
And a seasonal function which describe the laying rate as:
N
∑
i=
0
2
φ ( t)
= Exp(
−α
( t −180
− i365)
).
[1] Tiemi Takahashi, L., Maidana, N.A., Castro Ferreira Jr., W., Petronio, P.,
Yang, H.M. (2005). Mathematical models for the Aedes aegypti dispersal
dynamic: travelling waves by wings and wind. Bulletin of mathematical
biology 67. 509-528.
[2] Wilkinson, D., Smith, G.C. (2002). A model of the mite parasite, Varroa
Destructor on Honeybees (Apis mellifera) to investigate parameters
important to mite population growth. Ecollogical Modelling 148. 263-275.
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