Influence of the motion of individuals on the evolution of a sirs epidemy

GUSTAVO J. SIBONA; FERNANDO PERUANI; GUILLERMO TERRANOVA

BIOMAT 2011 International Symposium on Mathematical and Computational Biology

World Scientific

Año: 2012; p. 351 - 362

We analyze the in°uence of agent displacement on the propagation of diseases exhibiting SIRS dynamics. The infection process takes place in a system of self-propelled agents moving on a plane and interacting through volume exclusion. The disease transmission depends on the time elapsed during the physical contact between a healthy agent and an infected one. The model allows us to explore the effect of the space dynamics of individuals, in a wide range of systems (from non-spatial and lattice models, and from di®usive movement to ballistic). We show that the population dynamics can be described by mean-¯eld approaches, and give expressions for the endemic states, which are highly dependent on the spatial agent kinetics. In particular we study the role of agent speed and rate of direction change on the mean collision time. This time is the key parameter for disease transmission, and then of crucial importance to control the disease. We also show how the agent-agent interaction potential can be used as a control parameter to reduce the infected cases during the outbreak of a disease.