Modeling Sterile Mosquito Release to Control Disease

By Karthika Swamy Cohen

Mosquito-borne illnesses such as malaria, yellow fever, and Zika—which spread through human transmission via blood-feeding mosquitoes—present a serious public health concern in tropical and subtropical regions. While insecticide use can reduce the number of adult mosquitoes and control mosquito larvae, such chemical use in large amounts can lead to resistance of mosquitoes and affect human health. 

The use of sterile insects to curtail and eradicate mosquito populations has become more popular in recent years. Here, an overwhelming number of sterile male insects released into the wild compete with wild males to mate with females. When females mate with sterile males, no offspring are produced, thus reducing the reproductive output. Since sterile insects are not self-replicating, they are unable to establish themselves in the environment. 

Applying the sterile insect technique (SIT) by irradiation is complex and requires an intricate knowledge of the biology of the mosquito. The dose of radiation also varies based on the species – higher doses may negatively affect the lifespan and competivity of the male mosquitoes. Sterility can also be created by release of insects carrying a dominant lethal gene and by artificial infection by strains of Wolbachia, a diverse group of intracellular bacteria, where infected males make sperm that produce viable zygotes only with eggs from infected females.

Regardless of the method used to induce sterility, the challenge lies in determining suitable releasing strategies, since varying dynamics result from different methods used to release interactive wild and sterile mosquitoes leading to different transmission outcomes.

Mathematical models have been helpful in investigating and assessing the impact of releasing such sterile mosquitoes into the population. Delay and partial differential equation models have been used to investigate the effects of sterile mosquito release on the population dynamics of mosquitoes and transmission patterns of mosquito-borne diseases.

In a paper published recently in the SIAM Journal on Applied Dynamical Systems, Jicai Huang, Shigui Ruan, Pei Yu, and Yuyue Zhang revisit a previous mosquito population model with a nonlinear saturated release rate of sterile mosquitoes. 

The authors simplify the model by removing the restriction that sterile and wild mosquitoes have the same fitness. Their analysis then reveals that at some parameter values, the model exhibits multiple stable or unstable limit cycles. They demonstrate that both the interactive wild and sterile mosquitoes tend toward extinction when the initial mosquito population is outside the outer unstable limit cycle. The wild and sterile populations will tend to periodic fluctuations when the initial mosquito population is inside the outer unstable limit cycle and outside the inner unstable limit cycle. Finally, the wild and sterile mosquitoes will tend to a positive steady state when the initial mosquito population is inside the inner unstable limit cycle. 

Their analysis reveals that the mosquito population can be eliminated above a critical release rate coefficient of sterile mosquitoes. Below this coefficient, the interacting sterile and wild mosquitoes coexist in the form of multiple periodic oscillations and steady states in some initial populations. 

This study can lend a great deal of insight to agencies involved in designing sterile mosquito releasing policies for the control of disease.

Read the paper. 

Karthika Swamy Cohen is the managing editor of SIAM News.