Coronaviruses are a large family of viruses that cause different symptoms, from mild cold to severe respiratory distress, and they can be seen in different types of animals such as camels, cattle, cats and bats. Novel coronavirus called COVID-19 is a newly emerged virus that appeared in many countries of the world, but the actual source of the virus is not yet known. The outbreak has caused pandemic with 26,622,706 confirmed infections and 874,708 reported deaths worldwide till August 31, 2020, with 17,717,911 recovered cases. Currently, there exist no vaccines officially approved for the prevention or management of the disease, but alternative drugs meant for HIV, HBV, malaria and some other flus are used to treat this virus. In the present paper, a fractional-order epidemic model with two different operators called the classical Caputo operator and the Atangana–Baleanu–Caputo operator for the transmission of COVID-19 epidemic is proposed and analyzed. The reproduction number is obtained for the prediction and persistence of the disease. The dynamic behavior of the equilibria is studied by using fractional Routh–Hurwitz stability criterion and fractional La Salle invariant principle. Special attention is given to the global dynamics of the equilibria. Moreover, the fitting of parameters through least squares curve fitting technique is performed, and the average absolute relative error between COVID-19 actual cases and the model’s solution for the infectious class is tried to be reduced and the best fitted values of the relevant parameters are achieved. The numerical solution of the proposed COVID-19 fractional-order model under the Caputo operator is obtained by using generalized Adams–Bashforth–Moulton method, whereas for the Atangana–Baleanu–Caputo operator, we have used a new numerical scheme. Also, the treatment compartment is included in the population which determines the impact of alternative drugs applied for treating the infected individuals. Furthermore, numerical simulations of the model and their graphical presentations are performed to visualize the effectiveness of our theoretical results and to monitor the effect of arbitrary-order derivative.

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Background Multiple candidates of COVID-19 vaccines have entered Phase III clinical trials in the United States (US). There is growing optimism that social distancing restrictions and face mask requirements could be eased with widespread vaccine adoption soon. Methods We developed a dynamic compartmental model of COVID-19 transmission for the four most severely affected states (New York, Texas, Florida, and California). We evaluated the vaccine effectiveness and coverage required to suppress the COVID-19 epidemic in scenarios when social contact was to return to pre-pandemic levels and face mask use was reduced. Daily and cumulative COVID-19 infection and death cases from 26th January to 15th September 2020 were obtained from the Johns Hopkins University Coronavirus resource center and used for model calibration. Results Without a vaccine (scenario 1), the spread of COVID-19 could be suppressed in these states by maintaining strict social distancing measures and face mask use levels. But relaxing social distancing restrictions to the pre-pandemic level without changing the current face mask use would lead to a new COVID-19 outbreak, resulting in 0.8-4 million infections and 15,000-240,000 deaths across these four states over the next 12 months. Under this circumstance, introducing a vaccine (scenario 2) would partially offset this negative impact even if the vaccine effectiveness and coverage are relatively low. However, if face mask use is reduced by 50% (scenario 3), a vaccine that is only 50% effective (weak vaccine) would require coverage of 55-94% to suppress the epidemic in these states. A vaccine that is 80% effective (moderate vaccine) would only require 32-57% coverage to suppress the epidemic. In contrast, if face mask usage stops completely (scenario 4), a weak vaccine would not suppress the epidemic, and further major outbreaks would occur. A moderate vaccine with coverage of 48-78% or a strong vaccine (100% effective) with coverage of 33-58% would be required to suppress the epidemic. Delaying vaccination rollout for 1-2 months would not substantially alter the epidemic trend if the current non-pharmaceutical interventions are maintained. Conclusions The degree to which the US population can relax social distancing restrictions and face mask use will depend greatly on the effectiveness and coverage of a potential COVID-19 vaccine if future epidemics are to be prevented. Only a highly effective vaccine will enable the US population to return to life as it was before the pandemic.