论文标题
养鱼区域中疟疾动态的建模和控制
Modeling and control of malaria dynamics in fish farming regions
论文作者
论文摘要
在这项工作中，我们提出了一个代表鱼池，蚊子种群和疟疾传播之间关系的模型。 已经观察到，在巴西北部的Amazonic Acre地区，养鱼与疟疾的传播相关，当时是在人工池塘中进行的，这些池塘成为繁殖地。发现有证据表明，从农作物罐的边缘清洁植被有助于控制蚊子种群的大小。 我们使用我们的模型来确定养鱼实践对疟疾传播动态的有效贡献。该模型由一个普通微分方程的非线性系统组成，并在清洁时间跳跃，其充当冲动的控制。我们研究系统在清洁的强度和周期性功能以及参数值的功能方面的渐近行为。特别是，我们陈述了消除蚊子人口或持续存在的足够条件，并在其下消除了疟疾或流行。我们通过对具有凹形非线性的合作系统应用结果来证明我们的条件。
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.
