Estimation of Reproduction Number and Other Parameters with Bounded Constraints for COVID-19: A Modelling Case Study for Kazakhstan

This paper presents a mathematical model and a parameter estimation technique for predicting the evolution of COVID-19 pandemic. First, a modified SEIR (susceptible, exposed, infectious, and recovered) is introduced. This modified model can take into account the time-dependent characteristic of the parameters, which is an important factor of this epidemic. Based on the real data, the parameters of the model are estimated. 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.