Optimal control approach for establishing Wolbachia in wild population of Aedes aegypti mosquitoes

Abstract

Replacements of wild Aedes aegypti mosquitoes with Wolbachia-infected insects are becoming more and more socially accepted for controlling and preventing arboviral diseases in various areas invaded by this vector species worldwide. The main characteristics of this environmentally friendly technique are [1, 2, 3, 4]: it reduces the vectorial capacity of female mosquitoes, shortens the vector life expectancy, and reduces the overall vectorial density. In particular, the presence of Wolbachia in the vector's cells impedes it from developing a viral load sufficient for infecting human individuals through mosquito bites.

Additionally, the maternal transmission of Wolbachia, combined with the effect of cytoplasmic incompatibility (CI), facilitates the spread of Wolbachia infection in wild Aedes aegypti populations. However, these two principal features (maternal transmission of Wolbachia and CI reproductive phenotype) are sensitive to thermal stress. The latter may cause a partial loss of Wolbachia infection, known as imperfect maternal transmission and imperfect CI.

This presentation is focused on the population dynamics model of Wolbachia invasion bearing the imperfections mentioned above. Under this setting, the goal of Wolbachia-based control of arboviral infections consists in achieving the coexistence equilibrium with a high density of Wolbachia-infected mosquitoes and a low density of wild mosquitoes. Our model can also be adapted to two major Wolbachia strains, wMel and wMelPop, which are being tested in field releases.

To ensure the evolution towards the desired coexistence equilibrium, we employ the optimal control approach to design the release strategies of Wolbachia-carrying insects. The control intervention aim is two-fold: minimizing the overall number of released Wolbachia-infected mosquitoes while reducing the total intervention time. Our numerical simulations with parameters for two Wolbachia strains will display different scenarios of the tradeoffs between these two objectives to offer alternatives for policymaking.