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Mathematics Sheds Light on Effective Application of Sterile Insect Technique

By Lina Sorg

The sterile insect technique (SIT) is a biological procedure for pest control. This method involves several steps, including mass rearing of the targeted insects in a lab, sterilization of male pupae via ionizing radiation, and their ultimate release into a natural population. When sterile males mate with non-sterile females in the wild, the females do not produce offspring — thereby causing a progressive decay of the targeted pest/vector and reducing the population of the next generation.

Figure 1. Map of Réunion island, a volcanic island in the Indian Ocean that is an overseas department of France. Figure courtesy of Wikitravel and the Regional Council of Reunion.
During the 2023 International Congress on Industrial and Applied Mathematics, which is currently taking place in Tokyo, Japan, Yves Dumont of the French Agricultural Research Centre for International Development and the University of Pretoria used modeling, analysis, and simulations to assess the application of SIT in the context of fruit flies and mosquitoes. “The SIT is an old autocidal control method that is used in several countries throughout the world against certain pests and vectors,” Dumont said. He noted that although SIT is conceptually simple, its implementation in the field is actually quite challenging. As such, scientists engage in multiple field experiments, numerical simulations, and discussions to understand the reasons for potential failures and adjust accordingly. “I try to use mathematics to think in advance about issues of this application,” Dumont said.

Dumont then introduced two SIT projects with the Asian tiger mosquito (Aedes albopictus) and the oriental fruit fly (Bactrocera dorsalis) that are underway on Réunion: an island in the Indian Ocean that serves as an overseas department of France (see Figure 1). He focused most of his talk on his team’s sterilization efforts towards the oriental fruit fly (see Figure 2), which destroys a wide variety of agricultural crops in tropical areas of the world.

The release of sterile insects always involves some form of quality control (QC) to check the efficiency of sterile males in terms of lifespan, competitivity, and so forth. “QC includes the estimate of the level of sterility,” Dumont said. “In general, full sterility is not reached by irradiation and a small percentage of sperm is still fertile.” This percentage is called residual fertility and is represented by \(\varepsilon\). Dumont developed a generic model for different species of fruit flies that accounts for residual fertility as well as two additional considerations: 

  • Unlike mosquitoes, which only mate once during their lifetime, female fruit flies can mate multiple times; in fact, some fruit flies can re-mate every 10 to 15 days.
  • Females who mate with sterile males can change their refractory period and seek out additional mating opportunities.

Figure 2. Bactrocera dorsalis, also known as the oriental fruit fly, is an agricultural pest that destroys a wide variety of crops in tropical regions. Figure courtesy of Viwat Wornoayporn and the International Atomic Energy Agency and shared via the Attribution-ShareAlike 2.0 Generic (CC BY-SA 2.0) license.
He sought to study the impact of these behaviors on the release strategies of sterile males.

Next, Dumont shared a visual depiction of his resulting compartmental model that accounts for re-mating and residual fertility, with compartments for non-flying stages, wild males, females looking to mate, wild females that mate with wild males, wild females that mate with sterile males, and sterile males. He defined and computed the basic offspring number (the reproduction rate of the fruit fly population), noting that SIT introduces a strong Alee effect—a positive correlation between population density and individual fitness—where 0 is either locally or globally asymptotically stable, depending on the size of the release. He also identified the existence of a critical release rate; female mosquitoes that re-mate more quickly than normal necessitate the release of larger amounts of sterile males.

Dumont then shifted focus to address the impact of environmental parameters on SIT mosquitoes. He used a temperature- and rainfall-dependent SIT model with a rainfall parameter to account for the evolution of breeding sites (based on time of year and amount of precipitation) and ultimately reduce the associated epidemiological risk. Rainfall is particularly influential, and the SIT model indicated that that the best time for weekly small releases of sterile males is from June to late November because this range requires the fewest number of weeks to exert control. “It’s very difficult to be ready at the right time,” Dumont said, citing laboratory constraints with SIT. “It’s better to have six months where you can start the release rather than two or three months.”

Dumont concluded his presentation by reiterating the complexity of SIT, especially in the context of fruit flies due to the female re-mating factor and its connection to residual fertility. Given this re-mating propensity, researchers must continue to account for female behavior. “Specific observations are needed to evaluate the behavior of females when they mate with sterile males,” Dumont said. He hopes to conduct additional experiments that focus on the tendencies of female fruit flies, improve his current models by incorporating environmental parameters, and pursue more multidisciplinary projects and joint collaborations in this research area.

Lina Sorg is the managing editor of SIAM News.
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