Analysis of SIQR type mathematical model under Atangana-Baleanu fractional differential operator

Abstract

In the given manuscript, the fractional mathematical model for the current pandemic of COVID-19 is investigated. The model is composed of four agents of susceptible <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mi>S</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math> infectious <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mi>I</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:math> quarantined <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mi>Q</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> and recovered <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> cases respectively. The fractional operator of Atangana-Baleanu-Caputo <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>(</mml:mo><mml:mtext>ABC</mml:mtext><mml:mo>)</mml:mo></mml:mrow></mml:math> is applied to the considered model for the fractional dynamics. The basic reproduction number is computed for the stability analysis. The techniques of existence and uniqueness of the solution are established with the help of fixed point theory. The concept of stability is also derived using the Ulam-Hyers stability technique. With the help of the fractional order numerical method of Adams-Bashforth, we find the approximate solution of the said model. The obtained scheme is simulated on different fractional orders along with the comparison of integer orders. Varying the numerical values for the contact rate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ζ</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math> different simulations are performed to check the effect of it on the dynamics of COVID-19.