During recent decades the long-range rapidity correlations phenomenon was studied both experimentally and theoretically in relativistic nuclear physics. The correlations between the multiplicities (n-n) and the transverse momentum and the multiplicity (pT-n) of charge particles are analyzed in the framework of the simple string inspired model with two types of sources. The sources of the first type (primary emitters) correspond to the initial strings formed in a hadronic collision. We introduce the sources of the second type (secondary emitters), which imitate the appearance of the emitters of a new kind resulting from interaction (fusion) of the initial strings. The model enabled to describe effectively the influence of the string fusion effects on the strength both the n-n and the pT-n correlations. It was found that in the region, where the secondary emitters start to produce, the calculation results predict the non-monotonic behaviour of the n-n and pT-n correlation coefficients with the growth of the mea