Qualitative Study of a Novel Fractional-Order Epidemic Model with Nonmonotone Incidences, Level of Awareness, and Quarantine Class

During an epidemic outbreak, slowing the infection among the population can be achieved through two major approaches: raising awareness about the disease and quarantining the infected population. Elevating awareness levels among the population is essential for slowing down the infection. In this study, our goal is to propose and mathematically analyze a novel Caputo derivative-based fractional-order Susceptible–Aware–Infected–Quarantined–Recovered–Susceptible compartmental model. The model is developed by incorporating the level of awareness among the population, explicit non-monotone incidence rates for new infection cases, and a saturated quarantine rate for the infected population. Additionally, this study aims to capture the complex dynamics of infectious diseases in the absence of any vaccine to control the disease spread. The qualitative study of the model reveals two equilibria: an infection-free equilibrium and an endemic equilibrium. We obtain that the infection-free equilibrium is locally asymptotically stable when the basic reproduction number is below one. Furthermore, we investigate the model for the possible occurrence of multiple positive equilibria and examine the local stability of the endemic equilibrium, showing that it is locally asymptotically stable under certain conditions when the basic reproduction number is above unity. Finally, we present numerical simulations to support our analytical findings.