An integrated deterministic-stochastic approach for forecasting the long-term trajectories of COVID-19

The ongoing coronavirus disease 2019(COVID-19)pandemic is one of the major health emergencies in decades that affected almost every country in the world.As of June 30,2020,it has caused an outbreak with more than 10 million confirmed infections,and more than 500,000 reported deaths globally.Due to the unavailability of an effective treatment(or vaccine)and insufficient evidence regarding the transmission mechanism of the epidemic,the world population is currently in a vulnerable position.The daily cases data sets of COVID-19 for profoundly affected countries represent a stochastic process comprised of deterministic and stochastic components.This study proposes an integrated deterministic–stochastic approach to forecast the long-term trajectories of the COVID-19 cases for Italy and Spain.The deterministic component of the daily-cases univariate time series is assessed by an extended version of the SIR[Susceptible–Infected–Recovered–Protected–Isolated(SIRCX)]model,whereas its stochastic component is modeled using an autoregressive(AR)time series model.The proposed integrated SIRCX-AR(ISA)approach based on two operationally distinct modeling paradigms utilizes the superiority of both the deterministic SIRCX and stochastic AR models to find the long-term trajectories of the epidemic curves.Experimental analysis based on the proposed ISA model shows significant improvement in the long-term forecasting of COVID-19 cases for Italy and Spain in comparison to the ODE-based SIRCX model.The estimated Basic reproduction numbers for Italy and Spain based on SIRCX model are found to be 4.78 and 3.25,respectively.ISA model-based results reveal that the number of cases in Italy and Spain between 11 May,2020–9 June,2020 will be 10,982(6383–15,582)and 13,731(3395–29,013),respectively.Additionally,the expected number of daily cases on 9 July,2020 for Italy and Spain is estimated to be 30(0–183)and 92(0–602),respectively.