The compound KTi(SO4)(2)center dot H2O was recently reported as a quasi-one-dimensional spin-1/2 compound with competing antiferromagnetic nearest-neighbor exchange J(1) and next-nearest-neighbor exchange J(2) along the chain with a frustration ratio alpha = J(2)/J(1) approximate to 0.29 [G. J. Nilsen, H. M. Ronnow, A. M. Lauchli, F. P. A. Fabbiani, J. Sanchez-Benitez, K. V. Kamenev, and A. Harrison, Chem. Mater. 20, 8 (2008)]. Here, we report a microscopically based magnetic model for this compound derived from density functional theory (DFT) based electronic structure calculations along with respective tight-binding models. Our (LSDA+U-d) calculations confirm the quasi-one-dimensional nature of the system with antiferromagnetic J(1) and J(2), but suggest a significantly larger frustration ratio alpha(DFT) approximate to 0.94-1.4, depending on the choice of U-d and structural parameters. Based on transfer matrix renormalization group (TMRG) calculations we find alpha(TMRG) = 1.5. Due to an intrinsic symmetry of the J(1)-J(2) model, our larger frustration ratio alpha is also consistent with the previous thermodynamic data. To identify the frustration ratio alpha unambiguously, we propose performing high-field magnetization and low-temperature susceptibility measurements.