Maintaining consistent model parameters in long-run experiments is challenging. We study the multiple change-points detection problem from this viewpoint for an autocorrelated sample path of a binary response variable. The probabilities of success and correlation structure are linked to explanatory or control variables using a generalized linear model. A Bayesian paradigm is introduced here to estimate the unknown number and locations of change-points and an adaptive RJMCMC algorithm is presented to generate pseudo-random samples from the posterior distributions. This approach allows researchers to incorporate the experts' ideas into the analysis of such data. The features of the proposed method are examined via some simulation studies. We also apply the presented method to COVID-19 data from four countries to detect the change-points in the infection procedures in the presence of some explanatory variables.