Numerical assessment of multiple vaccinations to mitigate the transmission of COVID-19 via a new epidemiological modeling approach

Vaccines play a crucial role in mitigating the transmission of COVID-19. The primary objective of COVID-19 vaccination campaigns is to induce immunity in individuals, thereby reducing the risk of infection, severe illness, and subsequent transmission within communities. The present study mainly focuses on examining the impact of multiple vaccinations on the transmission dynamics of COVID-19 using a new epidemic modeling approach. The vaccinated individuals are divided into three subclasses according to their vaccination status. The primary, secondary and booster shots of COVID-19 vaccines are considered in the construction of the model. Initially, the model is constructed using classical integer order differential equations and basic necessary properties are carried out. Furthermore, utilizing a fractional and fractal-fractional epidemiological approach with an exponential kernel, the model is extended with these operators in order to provide insights into the potential benefits of this vaccination strategy in controlling the spread of the disease. The uniqueness and existence criteria of the fractional and fractal-fractional models are presented and an efficient numerical solution is investigated using the modified Adams-Bashforth method. The impact of both fractional (memory index) and fractal parameters is demonstrated graphically for R-0 < 1 and R-0 > 1 showing the converges of solution trajectories to the disease-free and endemic steady states respectively. Moreover, we examine the impact of various vaccination rates (first and second dose, and booster short) on the reduction and mitigation of the disease incidence.