Modified SEIAR infectious disease model for Omicron variants spread dynamics

The highly infectious and low-mortality Omicron variant of COVID-19 was identified in Botswana and reported to the WHO by South Africa. Spread dynamics is often used in the study of infectious diseases. Seasons, human contact, vaccination and other factors are the important factors affecting the spread of diseases. To better study the dynamical characteristics and predict the epidemic trend of the Omicron variants, we propose modified infectious disease models based on the SEIAR model, and examine the spread of the Omicron variants using mathematical modeling. We modify the traditional SEIAR model with incorporating a new factor: the number of vaccinations. The first modified model is referred to as the SUV 1st V 2nd IARD model, which is applicable to the period before the outbreak of Omicron. Given the high infectivity of the Omicron variants and the role of vaccinations in reducing the spread risk during the outbreak of Omicron, we further add a factor for vaccination booster and construct a new dynamical model different from SUV 1st V 2nd IARD model, called the SV 2nd V 3rd IARD model. Through stability analysis, we confirm the existence of the local asymptotic stability of the disease-free equilibrium point and the local equilibrium point under the given conditions for both SUV 1st V 2nd IARD model and SV 2nd V 3rd IARD model. Additionally, sensitivity analysis is performed on the basic regeneration number of both models. Parameter estimation and numerical simulations are conducted using the epidemic data from Tokyo, Japan. Through sensitivity analysis, we find that increasing vaccination rates and reducing human contact can reduce the number of infections and alleviate medical pressure. To prevent and control the epidemic, the government can minimize human contact and promote the necessity of vaccination to the public, as they can effectively improve individual immunity, reduce the risk of virus infection, and limit the virus spread.