Open AccessANALYSIS OF A POPULATION BIOLOGY MODEL DESCRIBING THE INTERACTION BETWEEN THE PARASITIC MITE, VARROA JACOBSONI OUDEMANS AND THE HONEY BEE, APIS MELLIFERA L., USING NONLINEAR DIFFERENCE EQUATIONS
Author(s) -
Mangum W.A.
Publication year - 1998
Publication title -
natural resource modeling
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.28
H-Index - 32
eISSN - 1939-7445
pISSN - 0890-8575
DOI - 10.1111/j.1939-7445.1998.tb00303.x
Subject(s) - varroa jacobsoni , varroa , biology , mite , honey bee , population , parasitism , zoology , botany , ecology , host (biology) , apidae , hymenoptera , demography , sociology
A summary of the derivation of two coupled nonlinear difference equations describing varroa mite parasitism of honey bees is presented. Assuming constant parameters, four cases are constructed by letting reproduction be present or absent and by letting worker bees with the ability to remove their parasites be present or absent. The linear stability analysis of these cases is presented, and, where possible, the biological interpretation of the mathematics is also included. For each case, the effect of varroa mite immigration on the population dynamics is also investigated.