Research On Two Types Of Mathematical Models Based On Practical Problems And Data

This article mainly research on two types of models based on practical problems.First of all,we introduce the fast and slow predator-prey dynamics with multiple refuges,and then study the transmission of schistosomiasis by monitoring data and Batbour's model in four provinces.The details are given as follows:1?We established a predator-prey model with multiple refuges for prey.Based on two different time scales,applying the singular perturbation techniques we anal-yse the dynamics on the slow system.The stability analyses are performed and Hopf bifurcation occurs when the threshold condition is greater than one value.It is shown that adding refuges for prey may lead to stability lost.Furthermore,the case of one refuge and multiple refuges are compared.It is found that he migration of prey among patches affects the dynamics of predator-prey system.The effect of the migration between open habitat and refuges is stronger than that of the migration among refuges for prey.The refuge size also infects the dynamics of predator-prey system.2?ccording to monitoring data of Anhui,Jiangxi,Hubei,Jiangsu Provinces from 2005 to 2010,in this paper the transmission of schistosomiasis are studied based on Barbour' s mathematical model.The values of the basic reproduction number and key parameters are obtained with two methods.The first method is to calculate directly by using the parameter values in references.The second one is to estimate parameter values by the methods of noise measurement and data smoothing and then to obtain new values of basic reproduction number.Comparing these two methods,we found the second method is good to fit the data.Finally,some numerical simulations are carried out to discuss the development trend of prevalence of humans and snails in each province.It is found that schistosomiasis in four provinces is expected to be eliminated if the standards of prevention and control are maintained or improved.Furthermore,the time needed is different in the different four provinces.