The logistic model has some limitations when applied to the sparse census data sets, typically available for developing countries. In such a situation, the relative growth rates (RGR) exhibit some unusual trends which are different from the common decreasing trend of logistic law. To explain such irregular trends we extend the logistic law by incorporating nonlinear positive and negative feedback terms. We performed RGR modelling as a function of time, as the size covariate model is not analytically solvable and the underlying model is better identifiable in the former case. It can also detect the demographic phase change point of developing country. Copyright © Taylor & Francis Group, LLC.