Modeling and analysis of Caputo-type fractional-order SEIQR epidemic model

Abstract

In this research, a susceptible-exposed-infected-quarantine-recovered-type epidemic model containing fractional-order differential equations is suggested and examined in order to better understand the dynamical behavior of the infectious illness in the presence of vaccination and treatments. The non-negative and bounded solutions of our proposed model are examined for existence and uniqueness. We investigate the explicit formulation of a threshold , often known as the basic reproduction number, using the next-generation matrix technique. Depending on the value of , one endemic equilibrium exists and is stable for , and one disease-free equilibrium (exist for all values of ) is stable for . This article has also noticed the emergence of a transcritical bifurcation. The relevance of using vaccination and treatments as controls has been met by formulating a fractional-order optimal control problem. The resulting theoretical conclusions are supported by a few numerical simulations. Ultimately, a global sensitivity analysis is carried out to identify the parameters that have the greatest influence.