Dynamic behaviors for fractional epidemiological model featuring vaccination and quarantine compartments

Humans have been affected by various epidemic diseases, mostly are airborne and exhibit high transmission rates. Given these nature properties, quarantine measures are essential to control the spread of the diseases effectively. Motivated by this fact, and due to the successful use of mathematical modeling, we investigate a SIR model with quarantine and vaccination compartments. This model uses a system of fractional differential equations (SIQVR-based) with specific parameters to track the dynamics of model variables. We examine the well-posedness and boundedness results via standard tools. An effective threshold parameter \(\mathcal {R}_0\) ${\mathcal{R}}_0$ is determined using a generation matrix and equilibrium points of the model are obtained. To effectively manage the transmission of infection within the outlined model, we employ the strategy of optimal control. This approach involves implementing control measures and interventions guided by mathematical optimization techniques to minimize the spread of disease. These control strategies may encompass vaccination campaigns, quarantine protocols, social distancing measures and other preventive actions. Further, to evaluate the effectiveness of proposed model and the applied optimal control strategy, we conduct a series of numerical simulations. Computational results involve running the model under different scenarios, considering a range of parameters and meticulously analyzing the resulting outcomes.