Vaccination, Lock-Down, Measures and Time-Varying Reproduction Number Based Estimation and Control of COVID-19 Outbreak in Turkey

Abstract

The COVID-19 outbreak continues to spread all over the world. In many countries, measures are being taken and vaccination studies continue due to the spread of different virus mutations. In order to facilitate the fight against the virus, the data collected from the beginning of the epidemic until today have been used to construct a mathematical model of the epidemic spread. In this study, it was aimed to introduce an extended version of a recent epidemic model that has been proposed, in which parameters such as vaccination rate, quarantine conditions and time-varying virus reproduction number are included. For in case of the reproduction number and some of the states are time-varying and difficult to measure, they are estimated by a recently introduced efficient nonlinear observer. The real-data validation of the estimations shows the accuracy of the mathematical model and indicates that the spread of the virus can be controlled by observer-based control. Therefore, a nonlinear model-predictive control is used to stabilize the dynamics of the outbreak while unmeasured dynamics and parameters are estimated by the designed observer. Numerical results were obtained for the daily vaccinated population of Turkey is 2.1 million individuals (w = 0.025) and 420 thousand individuals (w = 0.005), respectively. For w = 0.025, it is seen that the COVID-19 pandemic will completely terminate in nearly 600 days for the BNT162b2 vaccine and nearly 700 days for the CoronaVac vaccine. For w = 0.005, it can be said that herd immunity will be reached on average 1000 days after (March 2020) the first active case is reported in Turkey. In the light of the numerical results, depending on the different quarantine conditions and vaccination rates, the future course of the epidemic in Turkey can be determined. Finally, observer-based stabilization results can be used in other countries where similar measures and vaccination strategies are applied. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.