Fractional SIAQR model with time dependent infection rate

Abstract

In this study we have proposed the SIAQR model with time-dependent infection rate. The model’s well-posedness is demonstrated, and the proposed model is then extended to the fractional mathematical model by employing the Caputo-Fabrizio fractional derivative operator. We have also used the Lipschitz condition and the linear growth condition to determine the conditions under which the model has a unique solution. The numerical solutions are presented. Furthermore, using graphical representations we will see how the number of infected, recovered individuals vary as the order of fractional derivative varies.

2010 Mathematics Subject Classification:

• Primary 92B05
• 92C60
• Secondary 26A33

Keywords:

• Fractional derivative
• numerical solution
• SIAQR model
• existence and uniqueness

Acknowledgements

Authors are thankful to reviewers for their constructive comments to improve this article. The researchers would like to acknowledge the Deanship of Scientific Research, Taif University for funding this work.