This paper presents the assessment and forecasts of the transmission dynamics of  COVID-19 with the effects of time-dependent control actions using the data in Kazakhstan as a case study. First, a modified SEIRD (susceptible, exposed, infectious, recovered, and death) model is introduced. The SEIRD model is developed to take into account the time-dependent characteristics of the model parameters, especially on the ever-evolving value of the reproduction number, which is one of the critical measurements used to describe the transmission dynamics of this epidemic . The reproduction number alongside other key parameters of the model can  be estimated by fitting the model to real-world data using numerical optimisation techniques  . 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 has not been receiving much attention by the research community thus far . Finally, some forecasts are made using five scenarios with time-dependent control measures such that the effects of the control actions onto the transmission dynamics of the pandemic can be quantified and betterunderstood .
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 .
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