Study On The Stability Of Infectious Diseases Model With Media Infection In Hospital

With the increase of patients in hospital and in community clinic, as well as an increase in the number of susceptible population, types of pathogenic microorganism enriched and invasive treatment rose. In addition, the abuse of antibiotics, the poor management, and irrational distribution of small and medium-sized hospitals, as well as the neglect of health care workers are likely to cause nosocomial infection. Which lead to the increase of medical costs, extend the time for medical treatment, even can cause patients’ death. Thus the nosocomial infection has become a global concern. At the same time with outbreaks of infectious diseases, behavior of prevention and control in hospital plays a more important role in the disease control and communication. This paper studied the following dynamic model of infectious diseases.Firstly, Combined with media-cross infection in hospitals, the mathematical model establishes cross infection model with antibiotic-drug resistance that caused by healthcare workers, who play as vector of infection; getting threshold R₀ that controls popularity of disease; analyzing the stability of disease-free equilibrium and positive equilibrium under threshold R₀ condition. Furthermore, when R₀< 1, the disease-free equilibrium is globally stable and there is no cross infection when the number of healthcare workers and patients with drug-resistance bacteria is zero, and there is only one positive equilibrium E*when the mathematic model makes certain that threshold R₀> 1 is in globally stable situation and cross function of antibiotics-drug resistance is in smoothly development.Secondly, According to the mechanism and characteristics of in?uenza A（HIN1）,this essay constructed a mathematical model.Then,the article got a threshold R₀ indicating whether the disease had been controlled or not.At the same time,this essay used the prevention data of Beijing in 2009 when the epidemic broke out simulating the model.The parameters of the model,which got sensitivity analysis,are clear,and data source is reliable.The model re?ects the process of the epidemic spread, and intuitively describes the development of in?uenza A（HIN1）.Thus,this article is useful in providing decisions for the prevention and control of the epidemic.Finally,combined with the practical problems of drug-resistant bacteria cross infection in hospital,?nd that hospital disinfection,sterilization and its protective measures can reduce the virus spread, which play an inhibitory role. This paper establishes a cross infection model of drug resistant bacteria with saturation incidence rate, and obtains a threshold R₀ indicating whether the disease has been controlled or not. Furthermore,analyses the dynamic state of the disease-free equilibrium point under the condition of threshold. When the R₀> 1, there is only one positive equilibrium point, when R₀< 1, the equilibrium point E₀ is locally asymptotically stable.