COVID-19 Transmission

This research develops a mathematical model to better understand how COVID-19 spreads when vaccination is included as a control strategy. The population is divided into compartments, susceptible, exposed, infected, quarantined, vaccinated, and recovered, and their interactions are described using conformable fractional derivatives, which account for memory effects and more realistic disease dynamics. The basic reproduction number R_0​ is calculated using the next-generation matrix method to measure how easily the disease spreads. Sensitivity analysis identifies which parameters most strongly influence transmission, while local and global stability analyses show that if R_0<1, the disease-free state is stable and the infection will eventually die out. A finite difference numerical scheme based on the Taylor series is developed to solve the model accurately and ensure strong convergence. Overall, the study demonstrates that vaccination plays a critical role in reducing disease transmission and helps bridge the gap between theoretical modeling and practical public health strategies.