  This paper presents the assessment of time-dependent national-level
restrictions and control actions and their effects in fighting the COVID-19
pandemic. By analysing the transmission dynamics during the first wave of
COVID-19 in the country, the effectiveness of the various levels of control
actions taken to flatten the curve can be better quantified and understood.
This in turn can help the relevant authorities to better plan for and control
the subsequent waves of the pandemic. To achieve this, a deterministic
population model for the pandemic is firstly developed to take into
consideration the time-dependent characteristics of the model parameters,
especially on the ever-evolving value of the reproduction number, which is one
of the critical measures used to describe the transmission dynamics of this
pandemic. The reproduction number alongside other key parameters of the model
can then be estimated by fitting the model to real-world data using numerical
optimisation techniques or by inducing ad-hoc control actions as recorded in
the news platforms. In this paper, the model is verified using a case study
based on the data from the first wave of COVID-19 in the Republic of
Kazakhstan. The model is fitted to provide estimates for two settings in
simulations; time-invariant and time-varying (with bounded constraints)
parameters. Finally, some forecasts are made using four scenarios with
time-dependent control measures so as to determine which would reflect on the
actual situations better.
