控制草原鼠患模型

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。

The Model of Grassland Rodents Control

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.