To the best of the author's knowledge, this paper presents the first attempt to develop a mathematical model of the formation and growth of inclusions containing misfolded TATA-box binding protein associated factor 15 (TAF15). It has recently been shown that TAF15 inclusions are involved in approximately 10% of cases of frontotemporal lobar degeneration (FTLD). FTLD is the second most common neurodegenerative disease after Alzheimer's disease (AD). It is characterized by a progressive loss of personality, behavioral changes, and a decline in language skills due to the degeneration of the frontal and anterior temporal lobes. The model simulates TAF15 monomer production, nucleation and autocatalytic growth of free TAF15 aggregates, and their deposition into TAF15 inclusions. The accuracy of the numerical solution of the model equations is validated by comparing it with analytical solutions available for limiting cases. Physiologically relevant parameter values were used to predict TAF15 inclusion growth. It is shown that the growth of TAF15 inclusions is influenced by two opposing mechanisms: the rate at which free TAF15 aggregates are deposited into inclusions and the rate of autocatalytic production of free TAF15 aggregates from monomers. A low deposition rate slows inclusion growth, while a high deposition rate hinders the autocatalytic production of new aggregates, thus also slowing inclusion growth. Consequently, the rate of inclusion growth is maximized at an intermediate deposition rate of free TAF15 aggregates into TAF15 inclusions.