Abstract
Wolbachia is possibly the most studied reproductive parasite of arthropod species. It appears to be a promising candidate for biocontrol of some mosquito borne diseases. We begin by developing a sex-structured model for a Wolbachia infected mosquito population. Our model incorporates the key effects of Wolbachia infection including cytoplasmic incompatibility and male killing. We also allow the possibility of reduced reproductive output, incomplete maternal transmission, and different mortality rates for uninfected/infected male/female individuals. We study the existence and local stability of equilibria, including the biologically relevant and interesting boundary equilibria. For some biologically relevant parameter regimes there may be multiple coexistence steady states including, very importantly, a coexistence steady state in which Wolbachia infected individuals dominate. We also extend the model to incorporate West Nile virus (WNv) dynamics, using an SEI modelling approach. Recent evidence suggests that a particular strain of Wolbachia infection significantly reduces WNv replication in Aedes aegypti. We model this via increased time spent in the WNv-exposed compartment for Wolbachia infected female mosquitoes. A basic reproduction number R_0 is computed for the WNv infection. Our results suggest that, if the mosquito population consists mainly of Wolbachia infected individuals, WNv eradication is likely if WNv replication in Wolbachia infected individuals is sufficiently reduced.
Highlights
Wolbachia is a maternally transmitted intracellular symbiont, and it is the most common reproductive parasite infecting a significant proportion of insect species, see e.g. O’Neill et al (1997), Werren (1997)
The model captures many of the well-known key effects of Wolbachia infection, including cytoplasmic incompatibility, male killing, reduction in reproductive output and incomplete maternal transmission of the Wolbachia infection
We extended the sex-structured mosquito population model (2.2)–(2.5) to include West Nile virus, which is spread by birds and mosquitoes, treating WNv as an SEI infection for mosquitoes, and as an SEIR infection for birds
Summary
Wolbachia is a maternally transmitted intracellular symbiont, and it is the most common reproductive parasite infecting a significant proportion of insect species, see e.g. O’Neill et al (1997), Werren (1997). Tors, namely, strong CI, low fitness cost and high maternal transmission rate, were identified as drivers of a successful introduction of the new Wolbachia strain into an Aedes population To this end researchers have developed and analysed continuous age-structured population models for Wolbachia infection dynamics, which take the form of partial differential equations, see Farkas and Hinow (2010); which can often be recast as delay equations, see e.g. It was reported that particular strains of Wolbachia (completely or almost completely) block dengue virus replication inside the mosquito hosts, see for example (Blagrove 2012; Hoffmann 2011; Walker 2011) To this end Hughes and Britton (2013) developed a mathematical model for Wolbachia infection as a potential control tool for dengue fever. The full WNv model will naturally include the bird population, too
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