RANDOMIZED FRACTIONAL SEIR-VQHP MODEL WITH APPLICATIONS IN COVID-19 DATA PREDICTION

This paper is to investigate the extent and speed of the spread of the coronavirus disease 2019 (COVID-19) pandemic in the United States (US). For this purpose, the fractional form of the susceptible-exposed-infected-recovered-vaccinated-quarantined-hospitalized-social distancing (SEIR-VQHP) model is initially developed, considering the effects of social distancing, quarantine, hospitalization, and vaccination. Then, a Monte Carlo-based back analysis method is proposed by defining the model parameters, viz. the effects of social distancing rate (α), infection rate (β), vaccination rate (ρ), average latency period (γ), infection-to-quarantine rate (δ), time-dependent recovery rate (λ), time-dependent mortality rate (κ), hospitalization rate (ξ), hospitalization-to-recovery rate (ψ), hospitalization-to-mortality rate (ϕ), and the fractional degree of differential equations as random variables, to obtain the optimal parameters and provide the best combination of fractional order so as to give the best possible fit to the data selected between January 20, 2020 and February 10, 2021. The results demonstrate that the number of infected, recovered, and dead cases by the end of 2021 will reach 1.0, 49.8, and 0.7 million, respectively. Moreover, the histograms of the fractional order acquired from back analysis are provided that can be utilized in similar fractional analyses as an informed initial suggestion. Furthermore, a sensitivity analysis is provided to investigate the effect of vaccination and social distancing on the number of infected cases. The results show that if the social distancing increases by 25% and the vaccination rate doubles, the number of infected cases will drop to 0.13 million by early 2022, indicating relative pandemic control in the US. [ FROM AUTHOR] Copyright of Fractals is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

A proposed fractional dynamic system and Monte Carlo-based back analysis for simulating the spreading profile of COVID-19.

This paper presents a dynamic system for estimating the spreading profile of COVID-19 in Thailand, taking into account the effects of vaccination and social distancing. For this purpose, a compartmental network is built in which the population is divided into nine mutually exclusive nodes, including susceptible, insusceptible, exposed, infected, vaccinated, recovered, quarantined, hospitalized, and dead. The weight of edges denotes the interaction between the nodes, modeled by a series of conversion rates. Next, the compartmental network and corresponding rates are incorporated into a system of fractional partial differential equations to define the model governing the problem concerned. The fractional degree corresponding to each compartment is considered the node weight in the proposed network. Next, a Monte Carlo-based optimization method is proposed to fit the fractional compartmental network to the actual COVID-19 data of Thailand collected from the World Health Organization. Further, a sensitivity analysis is conducted on the node weights, i.e., fractional orders, to reveal their effect on the accuracy of the fit and model predictions. The results show that the flexibility of the model to adapt to the observed data is markedly improved by lowering the order of the differential equations from unity to a fractional order. The final results show that, assuming the current pandemic situation, the number of infected, recovered, and dead cases in Thailand will, respectively, reach 4300, 4.5 × 10 6 , and 36,000 by the end of 2021.

Network Autoregressive Model for the Prediction of COVID-19 Considering the Disease Interaction in Neighboring Countries.

Predicting the way diseases spread in different societies has been thus far documented as one of the most important tools for control strategies and policy-making during a pandemic. This study is to propose a network autoregressive (NAR) model to forecast the number of total currently infected cases with coronavirus disease 2019 (COVID-19) in Iran until the end of December 2021 in view of the disease interactions within the neighboring countries in the region. For this purpose, the COVID-19 data were initially collected for seven regional nations, including Iran, Turkey, Iraq, Azerbaijan, Armenia, Afghanistan, and Pakistan. Thenceforth, a network was established over these countries, and the correlation of the disease data was calculated. Upon introducing the main structure of the NAR model, a mathematical platform was subsequently provided to further incorporate the correlation matrix into the prediction process. In addition, the maximum likelihood estimation (MLE) was utilized to determine the model parameters and optimize the forecasting accuracy. Thereafter, the number of infected cases up to December 2021 in Iran was predicted by importing the correlation matrix into the NAR model formed to observe the impact of the disease interactions in the neighboring countries. In addition, the autoregressive integrated moving average (ARIMA) was used as a benchmark to compare and validate the NAR model outcomes. The results reveal that COVID-19 data in Iran have passed the fifth peak and continue on a downward trend to bring the number of total currently infected cases below 480,000 by the end of 2021. Additionally, 20%, 50%, 80% and 95% quantiles are provided along with the point estimation to model the uncertainty in the forecast.

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.