The Study Of Epidemic Model With Media And Age-structure On Complex Networks

The epidemic is always severely influencing the human public health and social har-mony.Therefore,in order to predict and control the pervade and spread of epidemic,many scholars make use of the mathematical methods.For example,they establish the differential,difference,integral,algebraic equations to study the stability of the model of epidemic.In this paper,we study the stability and bifurcation of the model of epidemic which is affected by the media coverage and age-structure on networks and give the results of the numerical simulation and sensitivity analysis.In Chapter 1,we introduce the research background,current situation,prior knowledge which is necessary for the paper of epidemic.In Chapter 2,since we take the natural death rate,the disease-related death rate,and the temporary immunity of the exposed individuals into consideration,we construct the SEIS epidemic model which is impacted by the media coverage on homogeneous mixture.Utiliz-ing the method of regeneration matrix calculates the basic regeneration number R₀.Employ-ing the Hurwitz criterion proves that the disease-free equilibrium P₀ is locally asymptotically stable when R₀<1,and the endemic equilibria P_i^*?i=1,2,3,4?are locally asymptotically stable when R₀>1.Building the suited Lyapunov functional demonstrates that the disease-free equilibrium P₀ is globally asymptotically stable when R₀<1.Using the center manifold and the normal form theory certifies that the model exhibits the forward and backward bifur-cation when R₀=1,and the model occurs the Hopf bifurcation when?increases and the?^**is crossed.Furthermore,we give the numberical simulation and sensitivity analysis.In Chapter 3,because we bring in the natural death rate,the disease-related death rate,and the temporary immunity and relapse of the removed individuals,we investigate the SIRS epidemic model which is influenced age-structure on heterogeneous networks.According to the biological significance,we legitimately define the basic regeneration number R₀.Tak-ing advantage of the Hurwitz criterion attests that the disease-free equilibrium E⁰is locally asymptotically stable when R₀<1,and the endemic equilibria E^**is locally asymptotically stable when R₀>1.Simultaneously we employ the fluctuation lemma so as to prove the globally asymptotical stability of the disease-free equilibrium E⁰.Firstly,we demonstrate the asymptotical smooth,uniformly weak and strong persistence of the endemic equilib-rium E^**.Next,By constructing the proper Lyapunov functional,we prove the globally asymptotical stability of the endemic equilibrium E^**.Furthermore,we give the numberical simulation and sensitivity analysis.Finally,due to the theoretical analysis and numberical simulation,we know that the media coverage and age-structure have a positive impact on the transmission of epidemic,and the model occurs the more complicated dynamic behavior.