It is on record that rolling out COVID-19 vaccines has been one of the fastest for any vaccine production worldwide. Despite this prompt action taken to mitigate the transmission of COVID-19, the disease persists. One of the reasons for the persistence of the disease is that the vaccines do not confer immunity against the infections. Moreover, the virus-causing COVID-19 mutates, rendering the vaccines less effective on the new strains of the disease. This research addresses the multi-strains transmission dynamics and herd immunity threshold of the disease. Local stability analysis of the disease-free steady state reveals that the pandemic can be contained when the basic reproduction number, \(R_{0}\) is brought below unity. The results of numerical simulations also agree with the theoretical results. The herd immunity thresholds for some of the vaccines against COVID-19 were computed to guide the management of the disease. This model can be applied to any strain of the disease.