A fractional order approach to modeling and simulations of the novel COVID-19

Abstract

The novel coronavirus (SARS-CoV-2.) has emerged and spread at fast speed globally; the disease has become an unprecedented threat to public health worldwide. It is one of the greatest public health challenges in modern times, with no proven cure or vaccine. In this paper, our focus is on a fractional order approach to modeling and simulations of the novel COVID-19. We introduce a fractional type Susceptible-Exposed-Infected-Recovered (SEIR) model to gain insight into the ongoing pandemic of COVID-19. Our proposed model incorporates transmission rate, testing rates, and transition rate (from asymptomatic to symptomatic population groups) for a holistic study of the coronavirus disease. The impacts of these parameters on the dynamics of the solution proles for the disease are simulated and discussed in detail. Furthermore, across all the different parameters, the effects of the fractional order derivative are also simulated and discussed in detail. Various simulations carried out enable us gain deep insights into the dynamics of the spread of COVID-19. The simulation results confirm that fractional calculus is an appropriate tool in modeling the spread of a complex infectious disease such as the novel COVID-19. In the absence of vaccine and treatment, our analysis strongly supports the significance reduction in the transmission rate as valuable strategy to curb the spread of the virus. Our results suggest that tracing and moving testing up has an important benefit. It reduces the number of infected individuals in the general public and thereby reduce the spread of the pandemic. Once the infected individuals are identified and isolated, the interaction between susceptible and infected individuals diminishes and transmission reduces. Furthermore, aggressive testing is also highly recommended.

Caputo fractional-order SEIRP model for COVID-19 Pandemic

“…In [97] , a susceptible-exposed-infected-isolated-recovered compartmental modeling framework with constant total population dynamics is used to construct a new SEIQR Caputo fractional order COVID-19 mathematical model. Owusu-Mensah and co-authors [98] , have also studied a new COVID-19 epidemic model using Caputo derivative in fractional calculus. The well-known and powerful generalized form of Adams Bashforth–Moulton iterative scheme was applied to numerically solve their formulated nonlinear fractional order differential equation model.…”

System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

“…Doing this will help reduce the severity of next coronavirus outbreaks. There have been many proposed mathematical models and analyses by a large number of infectious disease researchers on COVID-19 and similar diseases see [2][3][4][5][6][7][8][9][10][11]. Furthermore, some authors have proposed a SIR or related models for COVID- 19.…”

COVID-19 vaccination hesitancy model: The impact of vaccine education on controlling the outbreak in the United States

“…Mathematical models are powerful tools for investigating human infectious diseases, such as COVID-19, contributing to the understanding of infections’ dynamics, and can provide valuable information for public-health policymakers [8, 9]. Numerous mathematical models have been used to provide insights into public health measures for mitigating the spread of the coronavirus pandemic [10, 11, 12, 13]. For example, Eikenberry et al in [14] developed a mathematical model to assess the impact of mask use by the general public on the transmission dynamics of the COVID-19 pandemic.…”