Farkas JZ & Hinow P (2010) Structured and unstructured continuous models for Wolbachia infections. Bulletin of Mathematical Biology, 72 (8), pp. 2067-2088. http://www.springerlink.com/content/0092-8240; https://doi.org/10.1007/s11538-010-9528-1
We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont 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.
Wolbachia; Cytoplasmic incompatibility; Age-structured population dynamics; Stability analysis; Animal populations Mathematical models; Wolbachia
Bulletin of Mathematical Biology: Volume 72, Issue 8