Modeling the influence of Twitter in reducing and increasing the spread of influenza epidemics

A more realistic mathematical influenza model including dynamics of Twitter, which may reduce and increase the spread of influenza, is introduced. The basic reproductive number is derived 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. Our results show 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 while the impact posed by the negative information of Twitter on the influenza virus is still extraordinary.