How Does Vaccine-Induced Immunity Compare to Infection-Acquired Immunity in the Dynamics of COVID-19?

Abstract

Five years into the COVID-19 pandemic, the availability of effective vaccines has substantially reduced new cases, hospitalizations, and mortality. However, the waning of immunity has been a topic of particular interest in relation to disease control. The objective of this study is to investigate the impact of the decline in vaccine-induced immunity ( (Formula presented.) ) and infection-acquired immunity ( (Formula presented.) ) on disease dynamics. For this purpose, we use a compartmental model with seven compartments that accounts for differential morbidity, vaccination, and waning immunity. A compartmental model divides a population into distinct groups depending on their disease status. The temporal changes in the compartments are represented through ordinary differential equations (ODEs). The model is mathematically analyzed to show that a backward bifurcation (i.e., a perverse outcome) may occur when the vaccinated reproduction number ( (Formula presented.) ) is equal to unity. Both local and global sensitivity analysis on the reproduction number reveal that the vaccine efficacy, waning of vaccine-induced immunity, vaccine coverage rate, coefficients of transmissibility, and the recovery rate for mild infections are the most sensitive parameters. The global sensitivity analysis on the cumulative number of infections shows that (Formula presented.) and (Formula presented.) are both pivotal parameters, while (Formula presented.) has a higher influence. Simulations on infections and mortality suggest that the changes in (Formula presented.) result in dynamics that are more pronounced compared to the dynamics resulting from the changes in (Formula presented.), thus indicating the importance of the duration of infection-acquired immunity in disease spread.