I'm studying bacterial anti-phage defense system and want to investigate the time rate of Lambda phage lysogens formation after infection. To detect lysogens in liquid culture I'm using PCR and primers proposed in the article below - http://nar.oxfordjournals.org/content/22/25/5765.full.pdf

The problem I've encountered is that I always get a reaction product even from phage lysate. I obtain phage lysate in the following manner:

- I plate lysate with microbiological loop on the lawn of sensitive culture

- After ON incubation I collect the top agar (sometimes try to induce prophages with heat shock or UV), add 1/10 V of chlorophorm and vigorously shake the mixture on vortex

-C/f and discard agar, treat supernatant with clorophorm again 

-C/f and collect supernatant as lysate.

So, from this lysate I always have a PCR product for prophage, maybe it still contains a pieces of host DNA. Could you suggest a solution for obtaining a lysogenes-free lysate? Maybe it is worthy to re-precipitate phage particles with PEG? 

Also, I would be very grateful if somebody could tell me what is the timing of Lambda lysogens formation in Escherichia coli.

Thank you!