鱼类养殖区域疟疾动力学的建模与控制
Modeling and control of malaria dynamics in fish farming regions
AI总结：
针对阿克里州鱼塘滋生蚊虫并加剧疟疾传播的问题，本文建立带清理脉冲控制的非线性常微分方程模型，刻画养殖活动影响，并给出蚊虫消亡或存续、疟疾消除或地方化的充分条件。
摘要：
在本工作中，我们提出了一个表示鱼塘、蚊子种群与疟疾传播之间关系的模型。据观察，在巴西北部亚马孙地区的阿克里州，当鱼类养殖在人工池塘中进行而这些池塘成为蚊虫滋生地时，其与疟疾传播存在相关性。已有证据表明，清除养殖池边缘的植被有助于控制蚊子种群的规模。我们利用该模型确定鱼类养殖实践对疟疾传播动力学的实际贡献。该模型由一个非线性常微分方程组构成，并在清理时刻发生跳跃，这些跳跃充当脉冲控制。我们根据清理的强度和周期性以及参数取值研究系统的渐近行为。特别地，我们给出了蚊子种群被消灭或持续存在、疟疾被消灭或成为地方病的充分条件。我们应用具有凹非线性项的合作系统的相关结果证明了这些条件。
英文摘要：
In this work we propose a model that represents the relation between fish ponds, the mosquito population and the transmission of malaria. It has been observed that in the Amazonic region of Acre, in the North of Brazil, fish farming is correlated to the transmission of malaria when carried out in artificial ponds that become breeding sites. Evidence has been found indicating that cleaning the vegetation from the edges of the crop tanks helps to control the size of the mosquito population. We use our model to determine the effective contribution of fish farming practices on malaria transmission dynamics. The model consists of a nonlinear system of ordinary differential equations with jumps at the cleaning time, which act as impulsive controls. We study the asymptotic behaviour of the system in function of the intensity and periodicity of the cleaning, and the value of the parameters. In particular, we state sufficient conditions under which the mosquito population is eliminated or persists, and under which the malaria is eliminated or becomes endemic. We prove our conditions by applying results for cooperative systems with concave nonlinearities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
