STATIC AND DYNAMIC EPIDEMICS ON LOOPED CHAINS AND LOOPED TREES

The dynamic epidemic model [N. Vandewalle and M. Ausloos, J. Phys. A 2 9, 309 (1996)] considers the growth of a cluster in a medium containin g a fraction x of mobile ''particles'' that are pushed by a propagatio n front. This model is exactly solved here on various chains and trees that contain loops following an ''evolution matrix'' method. The exac t value for the percolation threshold x(c) and the critical exponents are calculated for static and mobile particles, respectively. Surprisi ngly, the mobile character of the particles affects the values of the critical exponents on chains but not on trees. Thus there is a nonuniv ersal behavior for dynamic epidemics even on d=1 lattices.