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Structured and unstructured continuous models for \(Wolbachia\) infections. (English) Zbl 1201.92044
Summary: 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.

MSC:
92C60 Medical epidemiology
92D30 Epidemiology
34D20 Stability of solutions to ordinary differential equations
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