Another set of assumptions in a model concerns the values that are given to the parameters. Examples of parameters include the probability of HIV transmission per sex act for an individual on ART, the fraction of patients still alive and on ART three years after ART initiation, and the annual population growth rate. It is essential for any modelling study to include a transparent listing of all model parameters, providing the following for each parameter: the name of the parameter; the mathematical symbol of the parameter (if appropriate); the meaning of the parameter in plain language; the value(s) assigned to the parameter (a point estimate and range/confidence interval as appropriate); and a contextual justification for used values, with references for the origins of the model parameter(s), and any relevant caveats (particularly important if more than one value for the model parameter exists or if the parameter is fit in the model or is derived from another modelling analysis).
This notion of justifying or formally “fitting” individual parameters—or a model in its entirety—to data covers many possibilities. As these also do not lie on a clear continuum from “rough heuristic/qualitative” to “formally rigorous and unbiased”, some ad hoc critical evaluation is appropriate for the most important inputs into any model. All model fitting relies on the notion of the likelihood of observing a set of data. There are then various possible approaches to (1) maximising the likelihood, i.e., selecting the particular model within which the data are most consistent, or (2) performing a sensitivity analysis, i.e., identifying ranges of model parameters that are consistent with the data and determining the relative importance of each model parameter. Note that the “likelihood function” itself can capture multiple sources of randomness, such as the usually unavoidable incompleteness of sampling and random effects in population processes themselves.
Some parameters, such as the mother-to-child HIV transmission rate under a particular care regimen, can be more or less directly “measured” in an appropriate (typically randomized) study, using observation and standard robust biostatistical methods, but there may be subtle artefacts. For example, using logistic regression to identify the characteristics of individuals that are associated with an HIV infection or transmission event may be misleading in ways that are seldom systematically explored in routine application, beyond noting the potential for “residual confounding”. A particular shape for a relationship between a predictor (such as viral load or age) and an outcome (transmission) is implicitly assumed, although it may be inappropriate—age in particular may correlate strongly with health status, but not necessarily monotonically.
For parameters where it is very difficult to obtain direct measurements, e.g., to capture behavioural dynamics such as risk reduction in the face of risk perception, heuristic parametrization may indicate which parameter sets are plausible and which are clearly at odds with data: a heuristically sensible model and a formally fitted model should be clearly distinguished, with sensitivity analyses where applicable.
Often the most important assumptions concern those specifying a simulated intervention, and it is recommended that these be prominently and exhaustively listed. For instance, if the intervention of interest relates to a policy change in ART, specifying a “coverage” and “efficacy” may not be enough: assumptions about enrolment rates, adherence, and retention, as well as behavioural characteristics (e.g., risk reduction or compensation) and demographic impacts (e.g., reduced mortality rates and increased size of the HIV-positive population) 
may need to be made explicit. These specifications should be documented over the time period of the model simulation, and, where relevant, for different substrata of the modelled population. If the work is specific to a country, then it is helpful to involve relevant stakeholders in the decisions taken about parameter values, and this process should be described. Such documentation also assists when modelling findings are subsequently used to inform decision-making in that setting