Epidemic SIRS dynamics in a system of mobile agents

F. PERUANI; G.J. SIBONA

Arica, Chile

Workshop; X Latin American Workshop on non-linear Phenomena: LAWNP’07; 2007

LAWNP

We study the propagation of diseases exhibiting a S-I-R-S dynamics in a system of self-propelled agents moving on a plane and interacting through volume exclusion. The infection transmition depends on the time elapsed during the physical contact between a healthy agent and an infected one. The disease dynamics is Poissonian by which an infected agent becomes first recovered and then healthy. The model allows us to explore a wide range of densities, bridging the gap between non-spatial and lattice models. We show that the population dynamics can be described by mean-field approaches, and give expressions for the endemic states which are highly dependent on the spatial agent kinetic. We study the role of the velocity of the agents and show that there exists a counter intuitive upper bound for the epidemic size, which prevents the disease to take over the entire system even when the agent-contact rate goes to infinity.