A modified SEIR model: stiffness analysis and application to the diffusion of fake news

In this work we propose a novel and alternative interpretation of the SEIR model, typically used in epidemiology to describe the spread of a disease in a given population, to describe the diffusion of fake information on the web and the consequent truth re-affirmation. We describe the corresponding system of ordinary differential equations, giving a proper definition of the involved parameters and, through a local linearization of the system, we calculate the so-called stiffness ratio, i.e. the ratio between the real parts of the largest and smallest eigenvalues of the Jacobian matrix of the linearized problem. A large gap in the spectrum of such a Jacobian matrix (i.e., a large stiffness ratio) makes the underlying differential problem stiff. So, we study and analyze the stiffness index of the SEIR model and, through selected numerical examples on real datasets, we show that the more the model is stiff, the faster is the transit of fake information in a given population.