To study the transmission dynamic of SARS-CoV-2 using nonlinear saturated incidence rate

In this work, we construct a new SARS-CoV-2 mathematical model of SQIR type. The considered model has four compartments as susceptible $$ , quarantine $$ , infected $$ and recovered $$ Here saturated nonlinear incidence rate is used for the transmission of the disease. We formulate our model first and then the disease-free and endemic equilibrium (EE) are calculated. Further, the basic reproduction number is computed via the next generation matrix method. Also on using the idea of Dulac function, the global stability for the proposed model is discussed. By using the Routh-Hurwitz criteria, local stability is investigated. Through nonstandard finite difference (NSFD) scheme, numerical simulations are performed. Keeping in mind the significant importance of fractional calculus in recent time, the considered model is also investigated under fractional order derivative in Caputo sense. Finally, numerical interpretation of the model by using various fractional order derivatives are provided. For fractional order model, we utilize fractional order NSFD method. Comparison with some real data is also given.