Research On Mathematical Models And Their Parameter Identification Of Ebola Epidemic

Ebola epidemic is an acute severe infectious disease,short course,rapid outbreak,high mortality,it not only affects people's lives,but also affects the country's economic development and social stability.Therefore,it is very important to study the infectious characteristics of Ebola epidemic.In this thesis,firstly,the mathematics model of Logistic and SIRD are established for the characteristics of the Ebola epidemic.Then the identification optimization model is established to determine the model parameters.Finally,the epidemic characteristics of Ebola epidemic is analyzed.The main contents of this thesis are as follows:1.For the infectious diseases of Ebola epidemic dynamics,in this thesis,the logistic model is first used to describe the Ebola epidemic.Then an identification optimization model that can determine the logistic model parameters of Ebola epidemic is established.Finally,parameter identification for the logistic model of Ebola epidemic is done by using the cumulative infection data of Ebola epidemic situation in Guinea,Sierra Leone and Liberia.The results show that there are big differences in the growth rate and inhibition constant of these infected countries.2.For the infectious diseases of Ebola epidemic dynamics,in this thesis,the SIRD mathematical model is first used to describe the Ebola epidemic.Then an identification optimization model that can determine the SIRD model parameters is established and analyzed.The results show that these countries have different infection situations of Ebola epidemic,and a control region with a shape can be obtained.It are proved that the flow-invariance of the system and weak-invariance of the system.