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The mathematical SHIR-model deals with complex system of virus infection divided on four parts of individuals named as follows: S - susceptible, H - hidden, I - infected, R - recovered. We propose the original essentially non-linear difference equations describing across mutual dependence and find the conditions ensuring existence of the limit cyclic trajectories. In our approach the hidden part, H, have more dangerous role in spreading of infection, than usually discussed so-called exposed individuals. We observe that cyclic states appear under rather specific demands on the system parameters.