Analysis and Optimal Control of a Fractional Order SEIR Epidemic Model With General Incidence and Vaccination

In this article, we present an analysis and optimal control investigation of a fractional order SEIR epidemic model with General Incidence and Vaccination. We utilize fractional calculus to account for memory effects and non-local interactions in the disease transmission process, enhancing the model's ability to capture real-world complexities. The utilization of fractional derivatives plays a crucial role in accounting for long-term memory in the system, allowing us to better understand the disease dynamics. Our analysis focuses on investigating the existence, uniqueness, and stability of equilibrium points while considering the impact of vaccination on the disease dynamics. Additionally, we develop an optimal control strategy to minimize the number of infected individuals over a given time horizon by optimizing the vaccination rate. Numerical simulations are performed to validate the theoretical results and demonstrate the effectiveness of the proposed optimal control strategy in mitigating the spread of the epidemic. The findings of this study contribute to a better understanding of the dynamics of fractional order SEIR epidemic models and provide insights into the design of efficient control measures for infectious diseases. The ability to accurately capture memory effects and non-local interactions through fractional derivatives opens up new possibilities for developing more robust and effective intervention strategies in public health settings.

Automated summary

In this article, an analysis and optimal control investigation of a fractional order SEIR epidemic model with General Incidence and Vaccination are presented. The utilization of fractional calculus enhances the model's ability to capture real-world complexities by accounting for memory effects and non-local interactions in the disease transmission process. The existence, uniqueness, and stability of equilibrium points are investigated, and the impact of vaccination on the disease dynamics is considered. Additionally, an optimal control strategy is developed to minimize the number of infected individuals by optimizing the vaccination rate.