We designed set of primers for certain virus. Fluorescent signals pops up in naive mice too! It is stable time-dependently. While signals are changing in infected mice time-dependently. Is it possible the primer recognize some normal genes of mice as well? 1) No contamination. 2) repeated 3 times. 3) DNA is obtained from serum (which should not carry DNA except the possible DNA of virus). 4) NTCs has no signal.
IF the reason is some non-specific binding, try to figure out the maximum annealing temperature that works with your specific target DNA PCR. If raising the annealing temperature of your PCR by a few degrees resolves non-specific binding, its a simple fix. If not, redesigning the primers, or longer primers + using a higher annealing temperature may resolve the issue. Good Luck.