An epidemic model based on individuals with movement characteristics

In this paper an SIS model on a mesh-free 2D plane is developed in order to find the relationship between epidemic spreading, translational speed and infectious radius. The results showed that susceptible and infective individuals ultimately continue to coexist. As time goes on the population size of infected individuals will eventually reach a dynamic equilibrium. Moreover, the equilibrium value shows a continuous phase transition with the increase of the infectious radius. Additionally, when the infectious radius is too small to induce the phase transition the mobility would have a negative effect on the epidemic spreading, while when the infectious radius is close to the radius causing phase transition the mobility would have a positive effect on the epidemic spreading, and when the infectious radius is larger the mobility would have no effect on it.