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.


92C60 Medical epidemiology
92D30 Epidemiology
34D20 Stability of solutions to ordinary differential equations
Full Text: DOI arXiv


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