Time-variant reliability-based prediction of COVID-19 spread using extended SEIVR model and Monte Carlo sampling

A probabilistic method is proposed in this study to predict the spreading profile of the coronavirus disease 2019 (COVID-19) in the United State (US) via time-variant reliability analysis. To this end, an extended susceptible-exposed-infected-vaccinated-recovered (SEIVR) epidemic model is first established deterministically, considering the quarantine and vaccination effects, and then applied to the available COVID-19 data from US. Afterwards, the prediction results are described as a time-series of the number of people infected, recovered, and dead. Upon introducing the extended SEIVR model into a limit-state function and defining the model parameters including transmission, recovery, and mortality rates as random variables, the problem is transformed into a reliability model and analyzed by the Monte Carlo sampling. The findings are subsequently given in the form of exceedance probabilities (EPs) of the three main outputs, namely, the maximum number of infected cases, the total number of recovered cases, and the total number of fatal cases. Afterwards, by incorporating time into the formulation of the reliability problem, the EPs are calculated over time and presented as 3D probability graphs, illustrating the relationship between the number of cases affected (i.e., infected, recovered, or dead), exceedance probability, and time. The results for the US demonstrate that, by the end of 2021, the number of the infected (active) cases decreases to 0.8 million and number of cases recovered and fatalities increases to 41.3 million and 0.6 million, respectively.