In experimental studies of asthma, murine models of allergic airway inflammatory disease have been used to elucidate the mechanisms underlying the immune responses of asthma and to identify and investigate new ways to control allergic inflammation. However, mice do not spontaneously develop asthma. To investigate asthma-related processes, an artificial asthma-like reaction must be induced in the mice airways. In this study, the model of allergic asthma used in mice was based on the sensitization and challenge protocol with the use of Ovalbumina (OVA) in both BALB/c and C57BL/6 mice. The evaluation of respiratory mechanics was performed using forced oscillation technique (FOT) using a small animal ventilator (SAV). The model adjusted for the mechanical impedance of the respiratory system was the constant phase model (CPM), where the impedance of the respiratory system is described using four parameters (R n , I, G and H). The bronchoprovocation challenge testing with Methacholine (MCh) is widely used in clinical and research environments to measure airway responsiveness. To describe the magnitude of the response of the respiratory system as a function of exposure to the stimulus or agonist (MCh) after a given exposure of time, dose-response curves are used. Related literature generally presents a value per dose, or concentration, and evaluates the entire curve based on these peak values (maximum effect). In this work, we sought to expand the use of dose-response curves obtained during brocoprovocation tests in mice beyond the maximum value of the parameters R n and G. The exponential decay behavior due to airway smooth muscle relaxation observed in the parameters R n and G, after presenting initial peaks that reflect the airway smooth muscle contraction induced by the agonist MCh, can be represented by decreasing exponential curves. Thus, regressions in the form of simple decreasing exponential and inverse Richards curve (descending) were fitted to the dose-response curves of the parameters R n and G for the following doses of MCh: PBS, 30, 100, 300 and 1000 µg/kg. The nonlinear regressions obtained were able to reproduce the values and behavior of the experimental data collected for the parameters R n and G, for the BALB/c and C57BL/6. The model using the inverse Richards curve resulted in a better fit to the experimental data for both strains of mice at all doses of the agonist MCh, being able to provide maximum values in order to distinguish between the Control and OVA groups even in the face of discarding the maximum value measured experimentally when adjusting the model. It is a robust and reliable method. Hence, avoiding the disposal of the dataset from experimental procedures with mice, mitigating the waste of animals and other resources according to the principles of the 3Rs (Refinement, Reduction and Replacement).