Vaccine breakthrough and rebound infections modeling: Analysis for the United States and the ten U.S. HHS regions

A vaccine breakthrough infection and a rebound infection cases of COVID-19 are studied and analyzed for the ten U.S. Department of Health and Human Services (HHS) regions and the United States as a nation in this work. An innovative multi-strain susceptible-vaccinated-exposed-asymptomatic-symptomatic-recovered (SVEAIR) epidemic model is developed for this purpose for a population assumed to be susceptible to n-different variants of the disease, and those who are vaccinated and recovered from a specific strain k(k ≤ n) of the disease are immune to present strain and its predecessors j = 1, 2, …, k, but can still be infected by newer emerging strains j = k + 1, k + 2, …, n. The model is used to estimate epidemiological parameters, namely, the latent and infectious periods, the transmission rates, vaccination rates, recovery rates for each of the Delta B.1.617.2, Omicron B.1.1.529, and lineages BA.2, BA.2.12.1, BA.4, BA.5, BA.1.1, BA.4.6, and BA.5.2.6 for the United States and for each of the ten HHS regions. The transmission rate is estimated for both the asymptomatic and symptomatic cases. The effect of vaccines on each strain is analyzed. Condition that guarantees existence of an endemic with certain number of strains is derived and used to describe the endemic state of the population.