控制草原鼠患模型

The Model of Grassland Rodents Control

文中采用3种方法分别进行经济效益和灭鼠效果的分析。模型1:自然生长状态下老鼠的生长模型,建立在没有使用任何灭鼠措施的情况下老鼠数量随时间的变化函数,用logistics模型来描述;模型2:采用灭鼠药模型,在模型1的logistics函数中加入制约老鼠生长的函数,并且它是一个随着时间变化而改变的函数,通过MATLAB求解得到灭鼠量、有效灭鼠时间及灭鼠费用;模型3:采用引入天敌模型,利用天敌和老鼠的数量变化引入Volterra的捕食-食饵模型,观察天敌与老鼠之间的变化趋势,进而可得出短期和长期的效果以及资金投入的情况;模型4:人工种植牧草模型,在logistics模型的基础上引入牧草阻滞系数m1(t),考虑牧草自身的生长和衰落,确定m1(t)是一个分段函数,通过MATLAB求解得到灭鼠量有效时间及其费用。

Three methods were adopted to analyze economic benefit and deratization effect.Model 1： The logistics model was adopted to describe the variation function of mouse quantity with time in the condition of without use any deratization measures;Model 2： Adding a constraint function which varied with time,deratization quantity,effective deratization time and cost were obtained through MATLAB program;Model 3： The variation trend between enemy and mouse was observed through introducing Volterra predator-prey model,then short-term,long-term effects and capital investment were obtained;Model 4： On the basis of logistics model,introducing pasture retardation factor,the effective time and cost of deratization quantity were obtained through MATLAB.