Telescopic observations and in situ measurements of the Io plasma torus show the density, temperature and composition to vary over time, sometimes up to a factor of 2. While previous models of the physical and chemical processes in the Io plasma torus have reasonably modeled the conditions of the Voyager 1 era, their authors have not addressed the observed variability nor explored the sensitivity of torus conditions to input parameters. In this paper we present a homogeneous torus model parameterized by five variables (transport timescale, neutral source strength, ratio of oxygen to sulfur atoms in the source, fraction of superthermal electrons, temperature of these hot electrons). The model incorporates the most recent data for ionization, recombination, charge exchange and radiative energy losses for the major torus species (S, S+, S++, S+++, O, O+, O++). We solve equations of conservation of mass and energy to find equilibrium conditions for a set of input parameters. We compare model plasma conditions with those observed by Voyager 1, Voyager 2 and Cassini. Furthermore, we explore the sensitivity of torus conditions to each parameter. We find that (1) torus conditions are distinctly different for the Voyager 1, 2 and Cassini eras, (2) unique torus input parameters for any given era are poorly constrained given the wide range of solution space that is consistent with the range of observed torus conditions, (3) ion composition is highly sensitive to the specification of a non-thermal electron distribution, (4) neutral O/S source ratio is highly variable with model values ranging between 1.7 for Cassini to 4.0 for Voyager conditions, (5) transport times range between 23 days for Voyager 2 to 50 days for Voyager 1 and Cassini, (6) neutral source strengths range between 7 to 30 ¿ 10-4 cm-3 s-1 which corresponds to a net production of 0.4 to 1.3 tons/s for a torus volume of 1.4 ¿ 1031 cm3, or 38 RJ3.