Two Kinds Of Transmission Dynamics Model Analysis Based On Detection Behavior

With the increasing of human communication,public health and the ability of network information management has a great influence on people,especially the significant influence on people’s physical and mental health.Therefore,the implementation of the disease prevention and control measures and the effective management of Internet rumors are particularly important.The paper,based on the above ideas,considering the detection of animals and information,establish some dynamics models about reflecting the spread of brucellosis and the spread of Internet rumors,and study the influnce on detection behaviors of two kinds of model dynamics behaviors.The specific content and target are as follows:In the second chapter,this paper establishes the human-animal dynamic transmission model of brucellosis with the number of infected patients as the detection information.The basic regeneration numberR₀ is given,whenR₀<1,Lyapunov function is constructed to proved that the disease-free equilibrium point is globally asymptotically stable,and whenR₀>1,the disease is uniformly persistent;In the last part,it is found through numerical simulation that periodic solutions will appear in the system when parameters meet certain conditions,which indicates that detection behavior can lead to complex transmission dynamics behaviors,which is unfavorable for disease prevention and control.In the third chapter,time-delay dynamic model is established with the number of infected patients as the detection information.The basic regeneration numberR₀ is given,whenR₀<1,Lyapunov function is constructed to proved that the disease-free equilibrium point is globally asymptotically stable,and whenR₀>1,the disease is uniformly persistent;At the same time,the condition of local stability of E^* is given for t=0,and the critical point of Hopf branch is given for t>0.In the last part,it is found through numerical simulation that for any giventvalue,when the detection rate （?） changes from small to large,Hopf branch will be generated.This shows that the influence of detection behavior on brucellosis cannot be ignored,and the time delay of latency will also affect the dynamic properties of the model.The fourth chapter takes the rumor characteristic vocabulary as the detection information,establishes the dynamics model to analyze the influence of information detection behavior on the network rumor propagation.The basic reproduction numbers R₀ is given.When R₀<1,the boundary equilibrium is globally asymptotically stable,and whenR₀>1,the positive equilibrium is globally attractive.Finally,the theoretical results are verified by numerical simulation.Finally,the article as a whole is summarized,and the dynamics transmission model of multi-patch brucellosis were established and sensitivity of the parameters were analysis based on the study of the paper,which provides a new idea for the study of the paper.