https://doi.org/10.1140/epjp/s13360-022-02603-z
Regular Article
A fractional-order mathematical model for COVID-19 outbreak with the effect of symptomatic and asymptomatic transmissions
1
School of Engineering, Monash University Malaysia, 47500, Subang Jaya, Selangor, Malaysia
2
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, 610054, Chengdu, Sichuan, People’s Republic of China
3
Department of Information Technology, Malaysia University of Science and Technology, 47810, Petaling Jaya, Selangor, Malaysia
Received:
16
February
2022
Accepted:
14
March
2022
Published online:
28
March
2022
The purpose of this paper is to investigate the transmission dynamics of a fractional-order mathematical model of COVID-19 including susceptible (
), exposed (
), asymptomatic infected (
), symptomatic infected (
), and recovered (
) classes named 
model, using the Caputo fractional derivative. Here, model describes the effect of asymptomatic and symptomatic transmissions on coronavirus disease outbreak. The existence and uniqueness of the solution are studied with the help of Schaefer- and Banach-type fixed point theorems. Sensitivity analysis of the model in terms of the variance of each parameter is examined, and the basic reproduction number 
to discuss the local stability at two equilibrium points is proposed. Using the Routh–Hurwitz criterion of stability, it is found that the disease-free equilibrium will be stable for 
whereas the endemic equilibrium becomes stable for 
and unstable otherwise. Moreover, the numerical simulations for various values of fractional-order are carried out with the help of the fractional Euler method. The numerical results show that asymptomatic transmission has a lower impact on the disease outbreak rather than symptomatic transmission. Finally, the simulated graph of total infected population by proposed model here is compared with the real data of second-wave infected population of COVID-19 outbreak in India.
© The Author(s) 2022
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