| Abstract: |
| \emph{Wolbachia}-based biocontrol has recently emerged as a potential method for prevention and control of dengue and other vector-borne diseases. Major vector species, such as \emph{Aedes aegypti} females, when deliberately infected with \emph{Wolbachia} become less capable of getting viral infections and transmitting the virus to human hosts.
\emph{Wolbachia} is a bacterial symbiont that is maternally transmitted from one generation to another through insect`s eggs and its spread among wild population is favored by a particular reproductive phenotype of cytoplasmic incompatibility. On the other hand, \emph{Wolbachia} may reduce the host lifespan and fecundity; therefore, population dynamics of \emph{Wolbachia} invasion usually exhibits very interesting features such as bistability and frequency-dependent Allee effect.
In this presentation, we propose and qualitatively analyze an explicit sex-structured population model for \emph{Wolbachia} invasion that describes an interaction of four mosquito compartments: \emph{Wolbachia}-infected and wild males and females. Further, we introduce a simplified two-dimensional variant of the original four-dimensional model in order to obtain better visualization of the \emph{Wolbachia} invasion dynamics, and to identify the minimum viable population size of wild mosquitoes. The latter is a threshold in frequency between wild and \emph{Wolbachia}-infected mosquitoes below which \emph{Wolbachia} gets established in local populations while wild mosquitoes become extinct. |
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