We consider a minimalist model for the Sterile Insect Technique (SIT), assuming that residual fertility can occur in the sterile male population. Taking into account that we are able to get regular measurements from the biological system along the control duration, such as the size of the wild insect population, we study different control strategies that involve either continuous or periodic impulsive releases. We show that a combination of open-loop control with constant large releases and closed-loop nonlinear control, i.e., when releases are adjusted according to the wild population size estimates, leads to the best strategy in terms of both number of releases and total quantity of sterile males to be released. Last but not least, we show that SIT can be successful only if the residual fertility is less than a threshold value that depends on the wild population biological parameters. However, even for small values, the residual fertility induces the use of such large releases that SIT alone is not always reasonable from a practical point of view and thus requires to be combined with other control tools. We provide applications against a mosquito species, Aedes albopictus, and a fruit fly, Bactrocera dorsalis, and discuss the possibility of using SIT when residual fertility among the sterile males, can occur.

中文翻译：

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通过不育昆虫技术进行非线性害虫/病媒控制：剩余生育力的影响

我们考虑了不育昆虫技术 (SIT) 的极简模型，假设在不育雄性种群中可以发生剩余生育力。考虑到我们能够在控制持续时间内从生物系统中定期测量，例如野生昆虫种群的大小，我们研究了不同的控制策略，包括连续或周期性的脉冲释放。我们表明，将具有恒定大释放量的开环控制和闭环非线性控制相结合，即当释放量根据野生种群规模估计进行调整时，在释放数量和总量方面都可以产生最佳策略将被释放的不育雄性。最后但并非最不重要的，我们表明，只有当剩余生育率小于取决于野生种群生物学参数的阈值时，SIT 才能成功。然而，即使对于很小的值，残余肥力也会导致使用如此大的排放量，以至于从实际角度来看，单独使用 SIT 并不总是合理的，因此需要与其他控制工具结合使用。我们提供了针对蚊子、白纹伊蚊和果蝇 Bactrocera dorsalis 的应用，并讨论了在不育雄性中可能发生残留生育力时使用 SIT 的可能性。