What is causing high levels of WBC/CRP/PCT for weeks?

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The patient is female, 78, and had a minor lung infection, but no/low fever. With more than 20 days of antibiotics, the WBC/CRP/PCT dropped from the peak but are still very high. They also fluctuating a lot. The doctors found baumannii but are not sure if that's the root cause.

Some test results below:

WBC#   24.28   13.07   20.42    16.19   19.31   16.72   19.92   9.66   14.4   18.51

Neut#   23.04   10.53   18.7     13.92    17.22    14.56   17.87  7.7    11.78   16.7

Neut%  94.9    80.6     91.6     86          89.2       87.1      89.7   79.7   81.8    90.2

PCT       11.25   3.06    2.09    0.701     2.01      0.586   0.464   0.227   0.228   0.359

Any thoughts are highly appreciated.