Sterile insect technique with accidental releases of sterile females. Impact on mosquito-borne diseases control when viruses are circulating.

The sterile insect technique (SIT) is a technique to control some vectors of diseases by releasing sterile males. However, during these releases, sterilized females can be (accidentally) released and since only females are vectors of diseases, it is important to study their impact when arthropod viruses are circulating. To that aim, we develop and study an entomological-epidemiological model, considering either permanent or periodic releases. Qualitative analyses of the continuous and periodic models are conducted. We highlight a critical sterile males release rate, Λ, above which the control of wild population is always effective, using massive releases. Estimating the basic reproduction number of the epidemiological model, R, we show that if it is above a certain threshold, R, that depends on the basic offspring number, N, and the release rate of sterile females, the epidemiological risk can only be controlled using (very) massive releases. Otherwise, we can estimate the basic reproduction number of the SIT epidemiological model, R, that shapes the stability property of the (periodic) disease-free equilibrium. We show that it might be possible to take R below 1 using non-massive, but large enough, releases. However, practically, it seems more efficient to consider massive releases, followed by small releases once the vector population is small enough. In addition to SIT, we also recommend mechanical control, i.e. the reduction of breeding sites, that greatly improves the efficacy of SIT, in terms of duration or size of the releases. Our results reveal that outside an epidemic period, the release of sterile females is not an issue, as long as the sterile males release rate is greater than Λ. Within an epidemic period, we show that sterile females releases do not really impact the SIT efficiency, as long as the release rate, Λ, is lower than a critical value, Λ, that depends on the mosquito and epidemiological threshold parameters, N, and R. To illustrate numerically our theoretical results, we consider Dengue parameters. We estimate all thresholds and also the effective reproduction number, R, and highlight the importance of early permanent or periodic SIT control to prevent or mitigate the risk of a Dengue epidemic, with and without sterile females releases.