Modeling And Analysis Of Seasonal Invasions Of Fall Armyworm

At the end of 2018,the fall armyworm has been discovered for the first time in Yunnan,China and rapidly spread to many provinces in China,the fall armyworm is harmful to agriculture and it is rated by the Food and Agriculture Organization of the United Nations as one of the top ten pests in the world,on June 2019,the Ministry of Agriculture and Rural Affairs and the Ministry of Finance allocated a special disaster relief fund of 500 million yuan for the prevention and control of the fall armyworm.However,the research on the fall armyworm is mainly analyzed from the aspect of ecological characteristics,so there are very few studies from the point of view of biological mathematics.Therefore,the main purpose of this paper is to establish a mathematical model as close as possible to the actual,which is important to control the fall armyworm.The main research contents of this article are as follow:Firstly,we formulate a seasonal influence mathematical model,in the form of delayed reactiondiffusion equation.Secondly,we applied the existing results to study the properties of global dynamics when the initial value of the model does not depend on the spatial variable.Finally,using the monotone dynamical system theory to analyze the spreading speeds and its expression is given of the initial case with compact supported.