A mathematical model reveals the influence of NPIs and vaccination on SARS-CoV-2 Omicron Variant

Abstract

An SVEIR SARS-CoV-2 Omicron variant model is proposed to provide some insights to coordinate non-pharmaceutical interventions (NPIs) and vaccination. Mathematically, we define the basic reproduction number and the effective reproduction number to measure the infection potential of Omicron variant and formulate an optimal disease control strategy. Our inversion results imply that the sick period of Omicron variant in the United States is longer than that of Delta variant in India. The decrease in the infectious period of the infection with infectiousness implies that the risk of hospitalization is reduced; but the increasing period of the infection with non-infectiousness signifies that Omicron variant lengthens the period of nucleic acid test being negative. Optimistically, Omicron’s death rate is only a quarter of Delta’s. Moreover, we forecast that the cumulative cases will exceed 100 million in the United States on February 28, 2022, and the daily confirmed cases will reach a peak on February 2, 2022. The results of parameters sensitivity analysis imply that NPIs are helpful to reduce the number of confirmed cases. In particular, NPIs are indispensable even if all the people were vaccinated when the efficiency of vaccine is relatively low. By simulating the relationships of the effective reproduction number , the vaccination rate and the efficacy of vaccine, we find that it is impossible to achieve the herd immunity without NPIs while the efficiency of vaccine is lower than . Therefore, the herd immunity area is defined by the evolution of relationships between the vaccination rate and the efficacy of vaccine. Finally, we present that the disease-induced mortality rate demonstrates the periodic oscillation and an almost periodic function is deduced to match the curve. A discussion completes the paper.

Higher COVID-19 Vaccination Rates Are Associated with Lower COVID-19 Mortality: A Global Analysis

“…A study by Wang and coworkers reported a mathematical model for the effect of vaccines and NPIs. They reported that even full vaccination at the population level was not sufficient for herd immunity when the efficiency of vaccines was low, and as such, NPIs were still indispensable [ 49 ]. A systematic review by Brito and coworkers reported that some less disruptive NPIs, such as mask wearing requirements, were also effective [ 50 ].…”

Revisiting the complex time-varying effect of non-pharmaceutical interventions on COVID-19 transmission in the United States

“…Consistent with previous studies, we found vaccination alone could not mitigate the epidemic, especially in the early stage of mass vaccination campaigns. Many modeling studies have emphasized the necessity of maintaining the intensity of NPIs when the vaccination coverage is low ( 10 , 16 , 20 ). A more important finding in this study was that mass vaccination campaigns in the early stage could even increase the risk of transmission.…”

“…Most previous studies focused on the early stage of the pandemic with the SARS-CoV-2 origin virus and the Alpha variant being dominant ( 3 , 17 , 18 ), however, evidence on the effectiveness in successive waves was relatively few, especially for the period of Omicron variant epidemic. Some modeling studies have discussed the varying effect of NPIs due to Omicron ( 19 , 20 ), but the clues were not strong enough because the assumed population features and transmission parameters would be different from the real world.…”

“…Further, how vaccines worked with NPIs to eliminate the epidemic was also poorly understood. Several previous studies have explored the potential of lifting NPIs as the vaccination coverage increased to a pre-set level via mathematical models ( 20–23 ). Many of these modeling studies have provided constructive suggestions on delaying the relaxation of NPIs, but the reliability of simulation evidence would be challenged by the uncertainty of real-world vaccine efficacy and the emergence of new variants ( 24 , 25 ).…”

A reliable numerical investigation of an SEIR model of measles disease dynamics with fuzzy criteria

“…A network model with periodic transmission rate was developed to analyze the effects of heterogeneity and waning immunity on measles transmission and to theoretically examine the threshold dynamics 28 . Mathematical modeling of infectious disease is studied a lot in recent times 29 – 35 , for example.…”