RESUMO
Coronavirus Disease 2019 (COVID-19) has spread the world resulting in detrimental effects on human health, lives, societies, and economies. The state authorities mostly take non-pharmacological actions against the outbreak since there are no confirmed vaccines or treatments yet. In this paper, we developed Suspicious-Infected-Death with Non-Pharmacological policies (SpID-N) model to analyze the properties of the COVID-19 casualties and also estimate the future behavior of the outbreak. We can state the key contributions of the paper with three folds. Firstly, we propose the SpID-N model covering the higher-order internal dynamics which cause the peaks in the casualties. Secondly, we parametrize the non-pharmacological policies such as the curfews on people with chronic disease, people age over 65, people age under 20, restrictions on the weekends and holidays, and closure of the schools and universities. Thirdly, we explicitly incorporate the internal and coupled dynamics of the model with these multi-dimensional non-pharmacological policies. The corresponding higher-order and strongly coupled model has utterly unknown parameters and we construct a batch type Least Square (LS) based optimization algorithm to learn these unknown parameters from the available data. The parametric model and the predicted future casualties are analyzed extensively.
RESUMO
Coronavirus disease (COVID-19) outbreak has affected billions of people, where millions of them have been infected and thousands of them have lost their lives. In addition, to constraint the spread of the virus, economies have been shut down, curfews and restrictions have interrupted the social lives. Currently, the key question in minds is the future impacts of the virus on the people. It is a fact that the parametric modelling and analyses of the pandemic viruses are able to provide crucial information about the character and also future behaviour of the viruses. This paper initially reviews and analyses the Susceptible-Infected-Recovered (SIR) model, which is extensively considered for the estimation of the COVID-19 casualties. Then, this paper introduces a novel comprehensive higher-order, multi-dimensional, strongly coupled, and parametric Suspicious-Infected-Death (SpID) model. The mathematical analysis results performed by using the casualties in Turkey show that the COVID-19 dynamics are inside the slightly oscillatory, stable (bounded) region, although some of the dynamics are close to the instability region (unbounded). However, analysis with the data just after lifting the restrictions reveals that the dynamics of the COVID-19 are moderately unstable, which would blow up if no actions are taken. The developed model estimates that the number of the infected and death individuals will converge zero around 300 days whereas the number of the suspicious individuals will require about a thousand days to be minimized under the current conditions. Even though the developed model is used to estimate the casualties in Turkey, it can be easily trained with the data from the other countries and used for the estimation of the corresponding COVID-19 casualties.