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

Abstract

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, $4.5\times {10}^6$ , and 36,000 by the end of 2021.