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

## TL;DR

This study compares how immunity from vaccines and infections affects the spread of COVID-19, finding that infection-acquired immunity has a stronger impact on disease dynamics.

## Contribution

The study introduces a compartmental model showing that waning infection-acquired immunity significantly influences disease spread more than vaccine-induced immunity.

## Key findings

- A backward bifurcation may occur when the vaccinated reproduction number (Rv) is equal to unity.
- Global sensitivity analysis shows that the waning of infection-acquired immunity (ω2) has a higher influence on cumulative infections than vaccine-induced immunity (ω1).
- Simulations indicate that changes in ω2 lead to more pronounced disease dynamics compared to changes in ω1.

## 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 (ω1) and infection-acquired immunity (ω2) 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 (Rv) 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 ω1 and ω2 are both pivotal parameters, while ω2 has a higher influence. Simulations on infections and mortality suggest that the changes in ω2 result in dynamics that are more pronounced compared to the dynamics resulting from the changes in ω1, thus indicating the importance of the duration of infection-acquired immunity in disease spread.