Before revision:  In this paper, the trust-region-reflective algorithm is applied for parameter estimation. After that, based on these calculated parameters, the prediction is made under three scenarios of the control measures and one scenario without any control measures. Unlike the previous models in which the effects of control action is not quantified, the proposed model can do this in order to better predict the evolution of this pandemic. The case study considers Kazakhstan, a badly affected country by this pandemic but do not receive enough considerations .
After revision:  In this paper, the trust-region-reflective (TTR) algorithm is used to fit the model to estimate both time-invariant and time-varying (with bounded contsraints) parameters. The model is verified using a case study based on the data in Kazakhstan, which is a country badly affected by this pandemic but do not receive enough considerations .