Linear and non-linear dynamics of the epidemics: System identification based parametric prediction models for the pandemic outbreaks

Coronavirus disease 2019 (COVID-19) has endured constituting formidable economic, social, educational, and phycological challenges for the societies. Moreover, during pandemic outbreaks, the hospitals are overwhelmed with patients requiring more intensive care units and intubation equipment. Therein, to cope with these urgent healthcare demands, the state authorities seek ways to develop policies based on the estimated future casualties. These policies are mainly non-pharmacological policies including the restrictions, curfews, closures, and lockdowns. In this paper, we construct three model structures of the S^pIⁿI^tI^bD-N (suspicious S^p, infected Iⁿ, intensive care I^t, intubated I^b, and dead D together with the non-pharmacological policies N) holding two key targets. The first one is to predict the future COVID-19 casualties including the intensive care and intubated ones, which directly determine the need for urgent healthcare facilities, and the second one is to analyse the linear and non-linear dynamics of the COVID-19 pandemic under the non-pharmacological policies. In this respect, we have modified the non-pharmacological policies and incorporated them within the models whose parameters are learned from the available data. The trained models with the data released by the Turkish Health Ministry confirmed that the linear S^pIⁿI^tI^bD-N model yields more accurate results under the imposed non-pharmacological policies. It is important to note that the non-pharmacological policies have a damping effect on the pandemic casualties and this can dominate the non-linear dynamics. Herein, a model without pharmacological or non-pharmacological policies might have more dominant non-linear dynamics. In addition, the paper considers two machine learning approaches to optimize the unknown parameters of the constructed models. The results show that the recursive neural network has superior performance for learning nonlinear dynamics. However, the batch least squares outperforms in the presence of linear dynamics and stochastic data. The estimated future pandemic casualties with the linear S^pIⁿI^tI^bD-N model confirm that the suspicious, infected, and dead casualties converge to zero from 200000, 1400, 200 casualties, respectively. The convergences occur in 120 days under the current conditions.