Colony Collapse Disorder (CCD) has become a global problem for beekeepers and for the crops that depend on bee pollination. While many factors are known to increase the risk of colony collapse, the ectoparasitic mite Varroa destructor is considered to be the most serious one. Although this mite is unlikely to cause the collapse of hives itself, it is the vector for many viral diseases which are among the likely causes for Colony Collapse Disorder. The effects of V. destructor infestation differ from one part of the world to another, with greater morbidity and higher colony losses in European honey bees (EHB) in Europe, Asia and North America. Although this mite has been present in Brazil for many years, there have been no reports of colony losses amongst Africanized Honey Bees (AHB). Studies carried out in Mexico have highlighted different behavioral responses by the AHB to the presence of the mite, notably as far as grooming and hygienic behavior are concerned. Could these explain why the AHB are less susceptible to Colony Collapse Disorder? In order to answer this question, we have developed a mathematical model of the infestation dynamics to analyze the role of resistance behavior by bees in the overall health of the colony, and as a consequence , its ability to face epidemiological challenges.