Optimal release programs for dengue prevention using Aedes aegypti mosquitoes transinfected with wMel or wMelPop Wolbachia strains.

In this paper, we propose a dengue transmission model of SIR(S)-SI type that accounts for two sex-structured mosquito populations: the wild mosquitoes (males and females that are Wolbachia-free), and those deliberately infected with either wMel or wMelPop strain of Wolbachia. This epidemiological model has four possible outcomes: with or without Wolbachia and with or without dengue. To reach the desired outcome, with Wolbachia and without dengue, we employ the dynamic optimization approach and then design optimal programs for releasing Wolbachia-carrying male and female mosquitoes. Our discussion is focused on advantages and drawbacks of two Wolbachia strains, wMelPop and wMel, that are recommended for dengue prevention and control. On the one hand, the wMel strain guarantees a faster population replacement, ensures durable Wolbachia persistence in the wild mosquito population, and requiters fewer releases. On the other hand, the wMelPop strain displays better results for averting dengue infections in the human population.

Robust viability analysis of a controlled epidemiological model.

Managing infectious diseases is a world public health issue, plagued by uncertainties. In this paper, we analyze the problem of viable control of a dengue outbreak under uncertainty. For this purpose, we develop a controlled Ross-Macdonald model with mosquito vector control by fumigation, and with uncertainties affecting the dynamics; both controls and uncertainties are supposed to change only once a day, then remain stationary during the day. The robust viability kernel is the set of all initial states such that there exists at least a strategy of insecticide spraying which guarantees that the number of infected individuals remains below a threshold, for all times, and whatever the sequences of uncertainties. Having chosen three nested subsets of uncertainties - a deterministic one (without uncertainty), a medium one and a large one - we can measure the incidence of the uncertainties on the size of the kernel, in particular on its reduction with respect to the deterministic case. The numerical results show that the viability kernel without uncertainties is highly sensitive to the variability of parameters - here the biting rate, the probability of infection to mosquitoes and humans, and the proportion of female mosquitoes per person. So, a robust viability analysis is a possible tool to reveal the importance of uncertainties regarding epidemics control.