Modeling SARS coronavirus-2 omicron variant dynamic via novel fractional derivatives with immunization and memory trace effects

Abstract

The objective of this paper is to recommend an adjusted Susceptible-Exposed-Infectious-Removed (SEIR) model that characterizes the temporal patterns of various individuals affected by the omicron variant in an epidemic. This model considers factors such as vaccination, asymptomatic cases, indoor and outdoor air, hospitalizations, and deaths, as well as the impact of immunization and memory trace. While many recent studies overlook the complexities of multiple strains, including their diverse transmission rates and reaction to vaccines, this study introduces a new fractional derivative model to examine the spread of the omicron variant of COVID-19 and the implementation of a vaccination campaign. A thorough theoretical analysis is conducted, and the critical factor (Rcrnz) is calculated using the model equations. It is demonstrated that when Rcrnz is less than 1, the disease-free state is globally asymptotically stable, meaning that the epidemic diminishes. Moreover, the stability of both global and local equilibrium points is examined. Numerical simulations are employed to demonstrate the alignment between the numerical findings and theoretical characteristics. The model is adjusted to experimental data that reflect the progression of the omicron variant of COVID-19 in Guangzhou, exhibiting a satisfactory performance in predicting the number of infected individuals, thereby suggesting its capability to accurately estimate asymptomatic cases. Furthermore, to emphasize the benefits of employing fractional differential equations, the paper provides examples related to memory trace and hereditary characteristics. Moreover, the examined models are expected to be applied and expanded upon in order to contribute to the formulation of policies for disease control during times of limited vaccine availability. To summarize, the model appears to be a sufficient tool for researching and managing infectious diseases. It is projected that as the Omicron variant's prevalence declines, there will be a reduced need for respiratory-focused precautions.