Abstract
Artificial releases of Wolbachia-infected Aedes mosquitoes have been under study in the past yearsfor fighting vector-borne diseases such as dengue, chikungunya and zika.Several strains of this bacterium cause cytoplasmic incompatibility (CI) and can also affect their host's fecundity or lifespan, while highly reducing vector competence for the main arboviruses. We consider and answer the following questions: 1) what should be the initial condition (i.e. size of the initial mosquito population) to have invasion with one mosquito release source? We note that it is hard to have an invasion in such case. 2) How many release points does one need to have sufficiently high probability of invasion? 3) What happens if one accounts for uncertainty in the release protocol (e.g. unequal spacing among release points)? We build a framework based on existing reaction-diffusion models for the uncertainty quantification in this context,obtain both theoretical and numerical lower bounds for the probability of release successand give new quantitative results on the one dimensional case.
Highlights
In recent years, the spread of chikungunya, dengue, and zika has become a major public health issue, especially in tropical areas of the planet [CDC16, BGB+13]
We address the question of the release protocol to guarantee a high probability of invasion
In the case of cytoplasmic incompatibility caused in Aedes mosquitoes by the endo-symbiotic bacterium Wolbachia, p is the proportion of mosquitoes infected by the bacterium (e.g. p = 1 means that the whole population is infected)
Summary
The spread of chikungunya, dengue, and zika has become a major public health issue, especially in tropical areas of the planet [CDC16, BGB+13]. This article studies a spatially distributed model for the spread of Wolbachia-infected mosquitoes in a population and its success as far as non-extinction probabilities are concerned. Models usually feature two stable steady states: invasion (the regular trait disappears) and extinction (the alternative trait disappears) Since this phenomenon is currently being investigated as a tool to fight Aedes transmitted diseases, the problem of determination of thresholds for invasion in this equation is of tremendous importance. In the case of cytoplasmic incompatibility caused in Aedes mosquitoes by the endo-symbiotic bacterium Wolbachia, p is the proportion of mosquitoes infected by the bacterium (e.g. p = 1 means that the whole population is infected) This frequency obeys a bistable reaction-diffusion equation. An appendix is devoted to the study of the minimization of the perimeter of release in one dimension
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