Functional Response Dynamics Analysis And Virulence Evolution Research Of Epidemic Model

Nowadays,the virulence evolution of ecological-epidemic and infectious epidemic evolution has been an important object in ecology and biology maths research.In the ecological environment,using combination method of the population dynamics and infectious epidemic dynamics,establishs three types of ecological-epidemic models with Holling functional response function.Based on the three types of ecological-epidemic models with Holling functional response function,the dynamic characteristic analysis and numerical simulation are explained phenomenon in ecological-epidemic.In the framework of adaptive dynamic methods,using the classic susceptible-infection-restoring host-pathogen(SIR)model explores the evolution of the pathogen virulence.In the dynamics analysis of infectious diseases,there are two different time scales: a quick ecological time scale and a slow evolutionary time scale.Three kinds of ecological-epidemic models with Holling functional response function is studied infectious epidemic dynamics mechanism in the ecological time scale in this paper.Classical SIR epidemic model is used to study adaptive evolution dynamic of pathogen virulence in the evolutionary time scale.Three ecological-epidemic models with Holling functional response function are studied in second chapter of this paper,obtaining main sufficient conditions for the robust stability of the system model in the balance,and using of Matlab has carried on the numerical simulation analysis of the system based on these conditions.The parameter b of three kinds of functional response functions and effective killing of force q E are mainly discussed,the two factors have influence on ecological-epidemic model.Through discussion,we found three types of ecological-epidemic models with Holling functional response function,under the influence of different parameters b and different effective killing of force q E,produce more complex dynamic graphics.In the framework of adaptive dynamic method(AD),by using a classic susceptible-infection-recovery(SIR)model,the evolution of the pathogen virulence has been discussed in the third chapter of this paper.The model assumes that the infection rate and recovery rate and pathogens virulence have important relations of compromise,but there is no virulence pathogenic factors of mortality,this was the key factor of virulence evolution dynamics.Through adaptive landscape of AD method,pairwise invadability plot and the evolutionary trajectory of the pathogen virulence,what has found that both certainty or random evolution path,pathogens with different initial virulence is convergence to a continuous and stable evolution on the singularity(CSS),that do not cause the complexity of the pathogen virulence evolution results.This phenomenon is due to not the result of the deadly virus.When there is the death rate,no complex evolution result may be caused,due to the population dynamics is the lack of adequate nonlinear correlation between variables.The results about how to reduce the pathogen of toxic harm to public health management,have provided a potential possibility.Dynamics analysis of three types of eco-epidemic models with the Holling functional response and evolutionary adaptation research of pathogen virulence based on the classical SIR epidemic model have been studied in this thesis.Through the analysis of the theoretical framework and different tools,that shows thought and result of epidemiological research in the different time scales.Epidemic system stability analysis in the traditional analysis has been expanded to pathogen virulence evolution research in evolution scales,that has an important theoretical basis and practical guiding significance for the guidance of public health management and disease prevention control.