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 (alpha), infection rate (beta), vaccination rate (rho), average latency period (gamma), infection-to-quarantine rate (delta), time-dependent recovery rate (lambda), time-dependent mortality rate (kappa), hospitalization rate (xi), hospitalization-to-recovery rate (psi), hospitalization-to-mortality rate (phi ), 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.