Atkinson Michael P, Su Zheng, Alphey Nina, Alphey Luke S, Coleman Paul G, Wein Lawrence M
Institute for Computational and Mathematical Engineering and Graduate School of Business, Stanford University, Stanford, CA 94305, USA.
Proc Natl Acad Sci U S A. 2007 May 29;104(22):9540-5. doi: 10.1073/pnas.0610685104. Epub 2007 May 22.
Motivated by the failure of current methods to control dengue fever, we formulate a mathematical model to assess the impact on the spread of a mosquito-borne viral disease of a strategy that releases adult male insects homozygous for a dominant, repressible, lethal genetic trait. A dynamic model for the female adult mosquito population, which incorporates the competition for female mating between released mosquitoes and wild mosquitoes, density-dependent competition during the larval stage, and realization of the lethal trait either before or after the larval stage, is embedded into a susceptible-exposed-infectious-susceptible human-vector epidemic model for the spread of the disease. For the special case in which the number of released mosquitoes is maintained in a fixed proportion to the number of adult female mosquitoes at each point in time, we derive mathematical formulas for the disease eradication condition and the approximate number of released mosquitoes necessary for eradication. Numerical results using data for dengue fever suggest that the proportional policy outperforms a release policy in which the released mosquito population is held constant, and that eradication in approximately 1 year is feasible for affected human populations on the order of 10(5) to 10(6), although the logistical considerations are daunting. We also construct a policy that achieves an exponential decay in the female mosquito population; this policy releases approximately the same number of mosquitoes as the proportional policy but achieves eradication nearly twice as fast.
鉴于当前控制登革热的方法失效，我们构建了一个数学模型，以评估一种释放携带显性、可抑制致死遗传性状纯合子的成年雄蚊策略对蚊媒病毒疾病传播的影响。一个关于成年雌蚊种群的动态模型被嵌入到一个用于疾病传播的易感-暴露-感染-易感人类-媒介流行病模型中，该模型考虑了释放的蚊子与野生蚊子之间对雌蚊交配的竞争、幼虫阶段的密度依赖性竞争以及幼虫阶段之前或之后致死性状的实现。对于释放的蚊子数量在每个时间点与成年雌蚊数量保持固定比例的特殊情况，我们推导出了疾病根除条件和根除所需释放蚊子的近似数量的数学公式。使用登革热数据的数值结果表明，比例策略优于释放蚊子数量保持恒定的释放策略，并且对于数量约为10⁵至10⁶的受影响人群，在大约1年内根除疾病是可行的，尽管后勤方面的考虑令人望而却步。我们还构建了一种能使雌蚊种群呈指数衰减的策略；该策略释放的蚊子数量与比例策略大致相同，但根除速度几乎快一倍。
