Research On Infectious Diseases Modeling

Infectious diseases have raged in all ages. In order to reduce the damage to human society from infectious diseases, the research on the infectious diseases is crucial. The study on epidemic diseases has been hundreds of years, the research based on epidemic model which is an important tool for analysis of epidemic spread rule, provides a reliable theroretical basis to control strategy of epidemic.At present, the research on epidemic dynamics based on models still has difficulties and areas to be improved, such as some epidemic models are too simple without considering the actual situation; The stability analysis on the endemic equilibrium point for the epidemic models with nonlinear incidence is a difficulty for epidemic research; The vehicle structure should also be considered into the study of epidemic dynamics; The analysis of the immune strategy form the perspective of theory should be strengthen and be discussed more deeply. The author had written this paper according to the insufficiency and difficulty of the resent research; The main content is as follows:(1) Introduced three classical epidemic models, through analyzing the classical SIS, SIR, SIRS epidemic models, the concept and method of the "compartment model" would be shown; The concept related to the dynamics of infectious diseases as well as the analysis method and the research object, purpose were given. A new modeling concept of combining the "compartment model" and complex network was put forward which was reflected in the following chapter.(2) Considering the recent research that assumed the epidemic completely led to the loss of fertility or the new individuals of infection’s would all be infectious, we put reproductive influence factor and infection probability of new individuals into an improved SIS model with vertical transmission and immigration; We solved the endemic equilibrium, analyzed the stability of the improved SIS model on disease-free equilibrium and endemic equilibrium, showed the expression of basic reproduction number, discussed the influence of reproductive factors as well as population immigration on disease spreading.(3) Considering the most of epidemic models whose incidence rate may greater than 1 which did not conform to the actual, we put forward a new nonlinear incidence rate from the probability point of view with which an improved SIRS epidemic model was brought out combining with the structure of uniform network and scale-free network. We showed the expression of general reproductive number, proved the existence and uniqueness of endemic equilibrium within the feasible region, analyzed the stability of improved system on disease free equilibrium and endemic equilibrium and discussed the SIRS spread raw on uniform network as well as the scale-free network; The simulation proved the validity of conclusion we have got. Considering fact that the individuals will take self-protections to prevent themselves from being infected when epidemic disease spread, we put forward an improved SIRS model with self-protection, analyzed the spreading law on uniform network, discussed the impact of self-protection on epidemic spreading.(4) Considering most of epidemic disease having the incubation period, we put forward an improved SEIRS model combining the structure of scale-free network based on existing models. Although the improved model was a little more complex than those were joined by time delay directly with nonlinear incidence rate which were difficultly analyzed, it was not only more convenient to research but eased the past assumptions to incidence rate. We analyzed the global stability of the improved SEIRS system on its equilibriums and took over the SEIRS spreading law on scale-free network which was supported by the simulation.(5) We further studied the impact of direct immunization on epidemic spreading combining the media and put forward improved SIRS epidemic models on homogeneous network as well as scale-free network; We analyzed the stability on equilibrium and solved the expression of general reproductive number; We also studied the SIRS model with isolation strategy which was introduced into the SIRS model mentioned in Chapter Four; We analyzed the impact of isolation through general productive number, which was supported by simulations.