Complex Dynamics In Social Epidemic Model With The Impact Of Twitter

Influenza and alcoholism have been having a far-reaching influence on human life. In medicine, alcohol abuse that is similar with pandemic virus has transmission and diffusion, that is, a person’s drinking behavior will affect their surrounding populations. In recent years, many scholars studied the dangers of alcohol abuse and flu to humans through the establishment of differential equation model approach,and got some control measures. Twitter as a social networking platform since it launched in 2006 has been widely used all over the world. Firstly, A more realistic mathematical influenza model including dynamics of Twitter, which may reduce and increase the spread of influenza, is introduced. Secondly, A novel alcoholism model which involves impact of Twitter is formulated, stability of multiple equilibria, Hopf bifurcation and forward and backward bifurcation were studied.In Chapter 1, we introduce some research backgrounds and current situation studied influenza and alcoholism, and some prior knowledge required for this study.In Chapter 2, we study a more realistic mathematical influenza model including dynamics of Twitter. The basic reproductive number is derived by using the next generation method and the stability of the steady states is proved. The existence of Hopf bifurcation are also demonstrated by analyzing the associated characteristic equation. Furthermore, numerical simulations and sensitivity analysis of relevant parameters are also carried out.In Chapter 3, a novel alcoholism model which involves impact of Twitter is formulated. It is shown that the model has multiple equilibria. Stability of all the equilibria are obtained in terms of the basic reproductive number R0. Using the way of the center manifold theory, the occurrence of backward and forward bifurcation for a certain defined range of R0 are established. Furthermore, the existence of Hopf bifurcation is also established by regarding the transmission coefficients β as the bifurcation parameter. Numerical simulations and sensitivity analysis on a few parameters are also carried out.Finally, the conclusion of the theoretical analysis and numerical simulation showed that the impact posed by the negative information of Twitter is not significant than the impact posed by the positive information of Twitter on influenza model and alcohol model while the impact posed by the negative information of Twitter on the influenza virus and alcohol behavior is still extraordinary.