Dynamic Study Of Ebola Virus Infectious Disease Model

Ebola virus appeared for the first time in various regions of Central Africa,with a very high mortality rate,resulting in a large number of human death.Most infected people are exposed to the virus when traveling to the affected areas,and they developed symptoms of Ebola virus fever after returning home.If the virus is not restricted,it may turn into a largescale epidemic and threaten the whole human race.In order to understand the transmission law of Ebola virus,this paper establish several kinds of Ebola virus epidemic models to study its transmission mechanism.The main work of this article is summarized as follows:Based on the SEIR model,a class of Ebola virus SEIQR models with vaccination and isolation measures are established.The basic reproduction number of the model is calculated,and the stability theory of the equilibrium of the model is given and proved.As an application of the model,the cumulative number of existing Ebola cases and models in Guinea are selected for fitting.Fitting results and actual cumulative data largely in line with Ebola patients.Further,by the sensitivity analysis of the parameters in the model,its turn out that raising the vaccination rate and isolation rate can effectively control the spread of Ebola virus,and further find that vaccination is more effective than isolation.Therefore,increasing vaccination could be a better strategy to control the spread of Ebola virus in real life.Based on the SIQR model,a model of Ebola SIQHR infectious disease with media coverage,isolation and hospitalization of inpatient treatment is established.Firstly,the basic regeneration number of the model is obtained by calculation.Secondly,the stability of the disease-free equilibrium and the endemic equilibrium is proved by constructing the Lyapunov function.Finally,numerical simulations verify the effects of media coverage,isolation and hospitalization on Ebola virus infectious diseases.Numerical simulation show that media coverage can effectively control the spread of Ebola virus.On the basis of the SIQHR model,adding the random noise,and the impact of random noise on infectious diseases is mainly analyzed.In other words,a stochastic SIQHR epidemic model with media coverage is discussed.Firstly,the existence and uniqueness of the global positive solution of the model are proved,according to the theory of stochastic differential equations and Lyapunov function method.Secondly,by constructing Lyapunov function and using It(?) formula,the sufficient conditions for the oscillation behavior of stochastic model near the equilibrium point of deterministic model,and the average persistence and extinction of disease are obtained.Finally,the theoretical results are verified by numerical simulation and the effect of random noise on infectious diseases is observed.