Generalized Mathematical Model of Infectious Disease During Medicinal Intervention by Employing Fractional Differential Equations

Emerging infectious diseases often arise, each presenting unique features and varying degrees of risk. In this study, we develop an extended SEIR model with six compartments and the Caputo fractional differential operator to examine the spread of COVID-19 in Malaysia during the vaccination campaign. The Adams–Bashforth–Moulton predictor–corrector approach is used to solve the model, resulting in accurate numerical simulations. We demonstrate fundamental mathematical features such as non-negativity, boundedness, equilibrium locations, and the basic reproduction number. We assess vaccination regimens' impact on disease transmission by calibrating the model using real-world data. Sensitivity and bifurcation studies show that vaccine efficacy, border control, and quarantine measures all play essential roles in disease mitigation. Notably, our findings show the occurrence of backward bifurcation, indicating that lowering the reproduction number to one is insufficient for disease elimination. These results provide vital insights into effective intervention.