A discrete proposal for modelling the infectious diseases expansion

This paper presents a new way to approach the dynamics of the infectious diseases expansion by means of a discrete space-time framework. A square grid represents the whole population and the links between the individuals (cell) are fixed by a connectivity pattern. This proposal lies in three points, a new neighborhood which is faster than the well-known Von Neumann and Moore neighborhoods, a set of local Boolean rules that define of the contacts between the neighborhood cells and a multi-grid implementation to cope with the delays between the sub-processes of the entire disease expansion. The main objective of this paper is modelling the different behaviors observed when solving the ordinary differential equations (ODE) of the Susceptible-Infectious-Recovered (SIR) and Susceptible-Infectious-Susceptible (SIS) models. Some real-world cases such as Influenza and Gastroenteritis are successfully modelled by our approach. This work contributes to draw equivalences between two conceptually different models and highlights that they give similar results by appropriately taking the parameter values.