Stability and Numerical Solutions of Second Wave Mathematical Modeling on COVID-19 and Omicron Outbreak Strategy of Pandemic: Analytical and Error Analysis of Approximate Series Solutions by Using HPM

Abstract

This paper deals with the mathematical modeling of the second wave of COVID-19 and verifies the current Omicron variant pandemic data in India. We also we discussed such as uniformly bounded of the system, Equilibrium analysis and basic reproduction number R0. We calculated the analytic solutions by HPM (homotopy perturbation method) and used Mathematica 12 software for numerical analysis up to 8th order approximation. It checked the error values of the approximation while the system has residual error, absolute error and h curve initial derivation of square error at up to 8th order approximation. The basic reproduction number ranges between 0.8454 and 2.0317 to form numerical simulation, it helps to identify the whole system fluctuations. Finally, our proposed model validated (from real life data) the highly affected five states of COVID-19 and the Omicron variant. The algorithm guidelines are used for international arrivals, with Omicron variant cases updated by the Union Health Ministry in January 2022. Right now, the third wave is underway in India, and we conclude that it may peak by the end of May 2022.

Fractal–fractional operator for COVID-19 (Omicron) variant outbreak with analysis and modeling

“…Given the vital role of intervention techniques, numerous analysts have achieved new epidemic models with several intervention techniques for COVID-19 in a homogeneous host population. The proposed model [30] has a total population of that is split into six compartments. The involved variables are can be illustrated as susceptible, exposed, infected, asymptotically infected, recovered and reservoir persons.…”

An Analytical Model for Confronting the Omicron Variant During COVID-19 Pandemic: A System Dynamic Approach

“…Due to the COVID-19 pandemic, researchers seek to realize how simulation instruments can help decision-makers deal with this very complex crisis [12]. Introduced by Foster, SD helps understand the relationships between the components of a system and represents dynamic behaviors through several feedback loops [34]. In particular, it is very beneficial as it enables policy-makers to accurately implement policies and detect their complex relationships, revealing the potential effects of alternative policies to make more efficient decisions [35].…”

Assessing the potential impact of COVID-19 Omicron variant: Insight through a fractional piecewise model

“…Since the outbreak of coronavirus, several mathematical models are proposed in various ways to control or reduce the risk of disease transmission worldwide. These includes the use integer and fractional modeling frameworks for different countries incorporating non-pharmaceutical interventions/vaccine [8] , environmental factors [9] , [10] , dead compartments [11] , Omicron variants [8] , [12] , [13] , [14] , social distancing [15] , optimal control [16] , [17] , super spreaders [18] . In particular, authors in [15] used an integer order model to quantify the effect of social distancing on the transmission dynamics of the coronavirus spread in South Africa.…”

“…In addition, other non-pharmaceutical measures may need to be reintroduced to prevent hospital admissions in England from exceeding those seen during the previous peak in winter 2020–2021. Few other fractional models and integer models [8] , [13] , [14] that have also modeled Omicron variant incorporating non-pharmaceutical interventions and vaccine [13] while in [8] the authors created and used real data from the United Kingdom to investigate the spread of COVID-19 with and without the Omicron variation and its connection with heart attack.…”