Dynamics of a Generalized Fractional Epidemic Model of COVID-19 with Carrier Effect

Abstract

Currently, coronavirus disease 2019 (COVID-19) continues to cause several new cases and deaths, and further new variants of the virus responsible this disease appear.
The present paper proposes a new mathematical model to understand the mechanisms
of the spread of COVID-19 and better describe its dynamics. The modes of infection
spread of COVID-19 via asymptomatic and symptomatic individuals are modeled by
two general nonlinear incidence functions in order to include several types of incidence
rates existing in the literature. When a disease outbreak within a community, individuals
acquire information about this disease. Therefore, the proposed model take into account
the memory effect on the outbreaks of COVID-19. This effect is modeled by a fractional
order derivative in Caputo sense. The mathematical analysis of the proposed model is
rigorously investigated, including the computation of the basic reproduction number R0
and the stability of equilibria.