  We introduce and investigate a series of models for an infection of a
diplodiploid host species by the bacterial endosymbiont \textit{Wolbachia}. The
continuous models are characterized by partial vertical transmission,
cytoplasmic incompatibility and fitness costs associated with the infection. A
particular aspect of interest is competitions between mutually incompatible
strains. We further introduce an age-structured model that takes into account
different fertility and mortality rates at different stages of the life cycle
of the individuals. With only a few parameters, the ordinary differential
equation models exhibit already interesting dynamics and can be used to predict
criteria under which a strain of bacteria is able to invade a population.
Interestingly, but not surprisingly, the age-structured model shows significant
differences concerning the existence and stability of equilibrium solutions
compared to the unstructured model.
