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This paper presents an update to the MK model [M. Kabirnezhad, Phys. Rev. D 97, 013002 (2018)], which was developed to describe single pion production in neutrino-nucleon interactions. Originally, the MK model used the helicity amplitudes and the hadronic current form factors of the Rein and Sehgal model [Ann. Phys. (N.Y.) 50, 189 (1968)]. The update includes a new definition for the helicity amplitudes in the first and second resonance regions and new vector-current form factors. Fits to electron-proton scattering data were used to determine these vector-current form factors and to assign errors to the constrained free parameters of the model. [ABSTRACT FROM AUTHOR]