Fractional view analysis of the impact of vaccination on the dynamics of a viral infection

Viral infections pose significant threats to public health globally. Understanding the behavior, transmission, and epidemiology of viruses is essential for developing strategies to prevent, control, and manage outbreaks. Mathematical models help in identifying emerging viral pathogens, assessing their risks, and implementing effective public health measures to mitigate their impact. In this work, we formulate the dynamics of Covid-19 viral infection with the effect of vaccination in fractional framework. Our study is mainly concerned with the dynamical behavior and qualitative analysis of Covid-19 dynamics. The model is investigated for basic properties and the threshold of the system is determined. To scrutinize the solution of the recommend system, we use the fixed point theorems of Schaefer and Banach to evaluate the existence and uniqueness of solutions. Moreover, sufficient conditions for the Ulam–Hyers stability of system is established through mathematical skills. We examine the solution pathways of our model through a numerical scheme to show the importance different input parameters of the system. Our findings emphasize the pivotal role of asymptomatic carriers and losing rate of immunity as critical determinants that can heighten the challenge of controlling Covid-19. Vaccination rate and the fractional parameters are attractive parameters while asymptotic fraction poses a significant risk since it has the ability to spread the illness to uninfected areas. We suggest that effective control of the transmission rate can effectively regulate the intensity of Covid-19 transmission.