Static and dynamic epidemics on looped chains and looped trees

The dynamic epidemic model [N. Vandewalle and M. Ausloos, J. Phys. A29, 309 (1996)] considers the growth of a cluster in a medium containing a fraction x of mobile ``particles'' that are pushed by a propagation front. This model is exactly solved here on various chains and trees that contain loops following an ``evolution matrix'' method. The exact value for the percolation threshold xc and the critical exponents are calculated for static and mobile particles, respectively. Surprisingly, the mobile character of the particles affects the values of the critical exponents on chains but not on trees. Thus there is a nonuniversal behavior for dynamic epidemics even on d=1 lattices. {} 1996 The American Physical Society.