Modeling COVID-19 and heart disease interactions through Caputo fractional derivative: memory trace analysis

The present work proposes a novel coronavirus model with heart disease using fractional order derivative (FOD). In this model, heart disease is treated as a comorbidity. The proposed model includes compartments such as exposed and infectious with and without comorbidities, hospitalized, and quarantined. System’s characteristics, such as existence-uniqueness, boundedness, and positivity of solutions, are illustrated. The proposed model parameters are modified to make fractional order model dimensionally consistent. The stability of disease-free (DF) equilibrium point is established using basic reproduction number ( \({R}_{0}).\) $R_0).$ Sensitivity analysis discusses impact of different parameters on disease transmission or control. Nonlinear least square optimization approach is employed to ascertain model parameters numerically. To numerically solve the proposed model, we use the predictor–corrector method. The simulated results are validated using actual data from India. The numerical findings for various FODs are obtained in the long run, which helps better analyze the actual situation. Furthermore, the impact of memory trace is presented for the proposed model to emphasize benefits of engaging FOD. The impact of parameters, such as quarantine rate \({(\mathfrak{g}}^{\upsilon })\) ${(\mathfrak{g}}^{\upsilon })$ and co-infection rate \({\mathcalligra{b}}_{2}^{\upsilon })\) ${\mathcal{b}}_2^{\upsilon })$ , is investigated through numerical simulations. The prospective model may reduce the worldwide medical difficulty of novel coronavirus and heart disease by optimizing simulation benefits.