Abstract
ABSTRACTA novel method to reduce the burden of dengue is to seed wild mosquitoes with Wolbachia-infected mosquitoes in dengue-endemic areas. Concerns in current mathematical models are to locate the Wolbachia introduction threshold. Our recent findings manifest that the threshold is highly dependent on the initial population size once Wolbachia infection alters the logistic control death rate of infected females. However, counting mosquitoes is beyond the realms of possibility. A plausible method is to monitor the infection frequency. We propose the concept of Wolbachia enhancing domain in which the infection frequency keeps increasing. A detailed description of the domain is presented. Our results suggest that both the initial population size and the infection frequency should be taken into account for optimal release strategies. Both Wolbachia fixation and extinction permit the oscillation of the infection frequency.
Highlights
The ability of Wolbachia to spread through cytoplasmic incompatibility (CI) [33,36] and grant mosquitoes resistant to dengue virus [2,21] has triggered the development of Wolbachia-based strategies for population replacement of Aedes mosquitoes, the primary vectors of dengue
Several key parameters are critical for determining the introduction threshold. (i) The intensity of CI sh, which is the probability of embryo death from the crossing of infected males with uninfected females; (ii) The maternal transmission leakage μ ∈ [0, 1], which is the percentage of uninfected progeny produced by an infected mother. (iii) The fitness cost/benefit, including changes in fecundity, hatching, pupation, eclosing and adult longevity, of infected females caused by Wolbachia infection
We offered a complete classification of the Wolbachia infection dynamics by the proof of a unique threshold curve, the separatrix of an unstable saddle point, the implication of results requires a knowledge of the initial population sizes x(0) and y(0)
Summary
The ability of Wolbachia to spread through cytoplasmic incompatibility (CI) [33,36] and grant mosquitoes resistant to dengue virus [2,21] has triggered the development of Wolbachia-based strategies for population replacement of Aedes mosquitoes, the primary vectors of dengue. By exploring the analytical property of the threshold curve, we find that with the presence of imperfect maternal transmission rate, Wolbachia in a completely infected population could be wiped out if the initial population size is small. All these findings point to the fact that even when μ = 0 which corresponds to perfect maternal transmission, there is no more single threshold infection frequency unless δ = 1, and the classical result of Turelli–Hoffman needs to be interpreted differently. These deceptive phenomena should be taken into account when designing release strategies to guarantee the success
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