Mathematics – Classical Analysis and ODEs
Scientific paper
2009-06-09
Bull. Math. Biol. 72 (2010), p. 2067-2088
Mathematics
Classical Analysis and ODEs
24 pages, 6 figures, revised and expanded
Scientific paper
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.
Farkas Jozsef Z.
Hinow Peter
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