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.

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.

Viable control of an epidemiological model.

In mathematical epidemiology, epidemic control often aims at driving the number of infected humans to zero, asymptotically. However, during the transitory phase, the number of infected individuals can peak at high values. Can we limit the number of infected humans at the peak? This is the question we address.