Dynamical Analysis Of Several Epidemic Models On Complex Networks

This thesis mainly discusses dynamical behavior of several kinds of epidemic spreading models.The full text can be divided into three parts: The first part is to consider an SIRS epidemic model with a general direct immunization rate on heterogeneous networks.We not only derived the epidemic threshold,but also analyzed the global stability of system equilibrium.The results improve and extend the previous work;The second part is to build an SIS epidemic model with local media coverage on networks and derive analytically the epidemic threshold;The third part is to study the SIS epidemic model on random and regular networks with general weight distribution.An edge-based compartment system is built by using pair approximation approach and a novel approach is developed to establish the epidemic threshold.We found that the linear and nonlinear transmission rates have different influences on the epidemic threshold.