Many models, such as the SIR (Susceptible, Infectious, Recovered) epidemiology model, consist of non-linear differential equations, involving unknown numerical parameters (e.g rate of propagation of a virus). Under conditions, it is possible to compute Input/Output (I/O) differential equations involving only the inputs (known quantity), the output (known measured quantity with noise) and the parameters. Those I/O equations can then be used to retrieve the values of the parameters from experimental curves. Instead of using differential equations, we consider integral equations. Indeed, in some examples, the introduction of integral equations increases the expressiveness of the models, improves the estimation of parameter values from error-prone measurements and reduces the size of the intermediate equations. Differential I/O equations can be automatically computed using differential elimination, with the DifferentialAlgebra in Maple. Integral I/O equations are more difficult to obtain. For the moment, we either integrate differential I/O equations (which sometimes require the computation of integrating factors) or perform an ad-hoc "integral" elimination. In my talk, I will first describe the computation of integral I/O equations using academic examples and present some partial results of the computation of integrating factors using deep learning. Then I will compare I/O equations of an academic example in terms of the quality of parameter estimation.