Mathematical Modeling And Analysis Of COVID-19: A Study Of New Variant Omicron

Abstract

We have devised an innovative mathematical framework to delve deep into the Omicron variant's behavior within the realm of COVID-19. Our model, a meticulous study of the Omicron variant, unfolds its mathematical implications. We've unraveled that this Omicron model maintains local asymptotic stability as long as the basic reproduction number (R0) stays below the critical threshold of 1. Remarkably, if R0 remains less than or equal to 1, our model gracefully attains global asymptotic stability, specifically at the disease-free equilibrium.

To unearth potential patterns of infection waves or stratification, we took a leap into the world of second-order differential equations. This expansion endowed us with a richer comprehension of the disease's dynamics and its inherent periodicity. We didn't stop there; we ventured into the realm of fractional stochastic modeling, conducting an extensive numerical analysis fueled by real-world data from South Africa spanning November 1, 2021, to January 23, 2022. Our model parameters were meticulously calibrated to mirror the actual scenario during that period, with an estimated basic reproduction number (R0) hovering around R0 ≈ 2.1107, mirroring South Africa's ground reality.

But we did not just crunch numbers; we dissected the data further to discern which factors exerted the most influence over R0. Employing the PRCC method in a global sensitivity analysis, we pinpointed the key drivers behind the virus's spread. These insights are invaluable for shaping targeted public health strategies that can either bolster or curtail the virus's transmission.

When it comes to simulating our model, we didn't rely on run-of-the-mill approaches. Instead, we harnessed a novel numerical scheme, meticulously tailored for solving piecewise fractional differential equations. Our simulations manifested as graphical representations that vividly underscore the effectiveness of adhering to recommended measures advocated by esteemed organizations such as the World Health Organization (WHO). These measures, including social distancing, mask-wearing, frequent handwashing, and avoiding gatherings, emerge as crucial tools for mitigating the infection's propagation within the population. 2010 AMS Classification: 93A30