Communication contains the immunology data treatment. New nonlinear methods of immunofluorescence statistical analysis of peripheral blood neutrophils have been developed. We used technology of respiratory burst reaction of DNA fluorescence in the neutrophils cells nuclei due to oxidative activity. The histograms of photon count statistics for the radiant neutrophils populations in flow cytometry experiments are considered. Distributions of the fluorescence flashes frequency as functions of the fluorescence intensity are analyzed. Square of deviations on the mean level of fluorescence flashes number considered as the probability measure of immunofluorescence fluctuations. Shannon information entropy, the square of fluctuations, their wavelet and wavelet spectra are investigated for medical diagnostics. Immunofluorescence fractal structure is analyzed for Hurst exponent and Shannon Weaver indices of biodiversity in the spaces of fluctuations, their wavelet and wavelet spectra. Biodiversity of fluorescence neutrophil populations has increasing tendency for oncology diseases, with anomalous increase of correspondence fractal dimension. We observe the universal exponential distribution of the central moments for information entropies. Parameters of exponential decrease are various for different health statuses. Therefore we have new tools to conduct diagnostics and monitoring of health statuses with the exponentially high sensitivity, precision and accuracy. Health or illness criteria are connected with statistics features of immunofluorescence histograms. Neutrophils populations fluorescence presents the sensitive clear indicator of health status.