Stability Analysis Of An Ebola Epidemic Model

At present,the Ebola virus is considered as one of the deadliest viruses.In order to reduce and control the accident rate of the Ebola virus,we analyze the Ebola infectious model in terms of dynamics and establish a human-animal couple model through Ebola transmission mechanism.Chapter 1 introduces the domestic and foreign research process of Ebola dynamics model.Then we present the main work of this paper.According to the transmission mechanism of Ebola virus,Chapter 2 establishes a human-animal couple Ebola transmission dynamics model involving vaccination and treatment.The basic reproduction number is obtained by the next generation matrix.Then we prove that when 0 < 1,the disease-free equilibrium point is globally asymptotically stable.In addition,the existence and global asymptotic stability of the coexistence equilibrium have been proved by the Lyapunov function and the La Salle invariant set principle.Finally the results have been verified by numerical simulation.In Chapter 3,in order to consider the impact of the media on Ebola virus,Chapter 3 establishes a human-animal couple Ebola transmission dynamics model with the impact of media coverage.The basic reproduction number is introduced by the next generation matrix,and the result is that the disease-free equilibrium is globally asymptotically stable when 0 < 1.In addition,the existence and global asymptotic stability of the coexistence equilibrium are proved by the comparison principle,the Lyapunov function and the La Salle invariant set principle.Finally,the results are verified by numerical simulation.Chapter 4 summarizes the main conclusions of this paper and presents some ideas for further study.