A Study On The Model Of Pest-control And Pollution-epidemic

The development of science and technology and the society, especially the the modern industry, destroys the ecological environment which keeps the human, animal and plant life alive, and poses numerous ecological problems. With the development of the biomathcmatics, more and more ecological problems can be dealt with mathematical model. Against the background of some increasingly serious ecological problems, in this thesis we develop a kind of pest control and pollution epidemic model and study the periodic solution to population extinction, global stability and conditions of persistence of the system.In Chapter 1, we introduce the background and give some theories of differential equation and relevant basic knowledge.In Chapter 2,in order to control pests, we can control the number of pests by releasing natural enemies. With the possibility of natural enemies being killed, we formulate a pest control model with time delay, impulse and stage structure, and obtain the threshold conditions under which pests go extinct or the system is permanent by controlling impulse period, and the number of natural enemies released and killed.The pests' extinction may interrupt the food chain, and it will cause another ecological problem, so we give the theorem of maintaining the mature pest population under the economic threshold level to control pests continuously at the end of the chapter.In Chapter 3,as for the problem of pollution and epidemic, since the population are infected with diseases or get killed by people in a polluted environment, we formulate a pollution ecology-epidemic model. In Section 1, we propose a model of population being constantly killed, and then we analyse the global asymptotic stability of equilibrium. Because the constant killing is practically impossible, we formulate the model with impulsive toxicant input and population being killed at different fixed time in Section 2, and then we obtain the threshold which can make the system permanent or extinct.Moreover, at the end of each chapter, we give some numeric simulation results which confirm the theoretical conclusions.