Some novel mathematical analysis on the fractional-order 2019-nCoV dynamical model

Area of Science:

• Epidemiology
• Mathematical Biology
• Fractional Calculus

Background:

• The global challenge of Covid-19 (2019-nCoV) since December 2019 necessitates effective control strategies.
• Mathematical modeling is crucial for simulating and understanding virus outbreak dynamics.
• Varying national control strategies have led to disparate outcomes in managing the pandemic.

Purpose of the Study:

• To analyze a fractional-order mathematical model for Covid-19 transmission dynamics.
• To compare the effectiveness of fractional-order models against integer-order models in simulating Covid-19 spread.
• To investigate the stability of equilibrium points within the fractional model.

Main Methods:

• Generalization of an existing integer-order Covid-19 model to a fractional-order model using the Caputo fractional derivative.
• Analysis of the stability of equilibrium points for the fractional model.
• Simulation and graphical representation of Covid-19 dynamics using daily and monthly case data.

Main Results:

• The fractional-order model provides a robust framework for analyzing Covid-19 dynamics.
• Stability analysis of equilibrium points was performed for the fractional model.
• Graphical analysis illustrated the time-dependent behavior of the virus spread.

Conclusions:

• Fractional-order models offer a more effective approach to simulating Covid-19 outbreaks compared to integer-order models.
• The study highlights the utility of fractional calculus in epidemiological modeling.
• Mathematical models, particularly fractional ones, are valuable tools for informing public health strategies against pandemics.