A mathematical model for COVID-19 transmission by using the Caputo fractional derivative

•COVID-19 is transmitted from asymptomatic individuals to susceptible individuals.•COVID-19 is transmitted from symptomatic individuals to susceptible individuals.•Since R0=1.6 is greater than 1, the COVID-19 will spread exponentially.•If COVID-19 is not controlled, it is estimated that about 20 million people will become infected in the next three years. We present a mathematical model for the transmission of COVID-19 by the Caputo fractional-order derivative. We calculate the equilibrium points and the reproduction number for the model and obtain the region of the feasibility of system. By fixed point theory, we prove the existence of a unique solution. Using the generalized Adams-Bashforth-Moulton method, we solve the system and obtain the approximate solutions. We present a numerical simulation for the transmission of COVID-19 in the world, and in this simulation, the reproduction number is obtained as R0=1:610007996, which shows that the epidemic continues.