Research On The Mathematical Models Of Hand Foot Mouth Disease And Tuberculosis In Beijing

Hand foot mouth disease and tuberculosis are the national notifiable diseases which need to be real-time monitored and intervened by Beijing Center for Diseases Prevention and Control and they are fast spreading, wide spreading and serious, etc. The spreading of hand foot mouth disease and tuberculosis are influenced by temperature, humidity, light and other seasonal factors, so that the transmission and outbreaks of those diseases have a certain periodicity. It has a great practical significance to prevent and control hand foot mouth disease and tuberculosis in Beijing by building the corresponding mathematical models for studying propagation of those seasonal diseases. At present, most papers research on hand foot mouth disease and tuberculosis in Beijing from statistical view, but little papers research by using mathematic model. In this situation, this paper builds cycle models for hand foot mouth disease and tuberculosis in Beijing and research on these two diseases.First, based on models of hand foot mouth disease and tuberculosis, this paper proof that when the basic reproduction number R0< 1, there exist a global asymptotic stability disease-free equilibrium and when the basic reproduction number R0> 1, there exist a positive periodic solution. By using Matlab, this paper calculated the basic reproduction number R0 of hand foot mouth disease in Beijing is 1.0195 and the basic reproduction number R0 of tuberculosis in Beijing is 1.0517. So that, the hand foot mouth disease and the tuberculosis will still exist in the future. This paper also gives the numerical simulation figures of hand foot mouth disease and tuberculosis in Beijing. To a certain extent these figures can descript the spread cases of hand foot mouth disease and the tuberculosis in Beijing.Second, this paper presents a method for using genetic algorithms to solve the least squares problem of cycle model’s parameters and illustrates advantages of this method to other paper which were using the non-linear least squares method. This paper also discusses of using the bootstrap statistical method to hypothesis test the parameter of the model, we can make a choice to accept or reject this parameter.