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The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is responsible for coronavirus disease-19 (COVID-19). This virus has caused a global pandemic, marked by several mutations leading to multiple waves of infection. This paper proposes a comprehensive and integrative mathematical approach to the third wave of COVID-19 (Omicron) in the Kingdom of Saudi Arabia (KSA) for the period between 16 December 2022 and 8 February 2023. It may help to implement a better response in the next waves. For this purpose, in this article, we generate a new mathematical transmission model for coronavirus, particularly during the third wave in the KSA caused by the Omicron variant, factoring in the impact of vaccination. We developed this model using a fractal-fractional derivative approach. It categorizes the total population into six segments: susceptible, vaccinated, exposed, asymptomatic infected, symptomatic infected, and recovered individuals. The conventional least-squares method is used for estimating the model parameters. The Perov fixed point theorem is utilized to demonstrate the solution's uniqueness and existence. Moreover, we investigate the Ulam–Hyers stability of this fractal–fractional model. Our numerical approach involves a two-step Newton polynomial approximation. We present simulation results that vary according to the fractional orders (γ) and fractal dimensions (θ), providing detailed analysis and discussion. Our graphical analysis shows that the fractal-fractional derivative model offers more biologically realistic results than traditional integer-order and other fractional models. [ABSTRACT FROM AUTHOR]

Natural symmetry exists in several phenomena in physics, chemistry, and biology. Incorporating these symmetries in the differential equations used to characterize these processes is thus a valid modeling assumption. The present study investigates COVID-19 infection through the stochastic model. We consider the real infection data of COVID-19 in Saudi Arabia and present its detailed mathematical results. We first present the existence and uniqueness of the deterministic model and later study the dynamical properties of the deterministic model and determine the global asymptotic stability of the system for R 0 ≤ 1 . We then study the dynamic properties of the stochastic model and present its global unique solution for the model. We further study the extinction of the stochastic model. Further, we use the nonlinear least-square fitting technique to fit the data to the model for the deterministic and stochastic case and the estimated basic reproduction number is R 0 ≈ 1.1367 . We show that the stochastic model provides a good fitting to the real data. We use the numerical approach to solve the stochastic system by presenting the results graphically. The sensitive parameters that significantly impact the model dynamics and reduce the number of infected cases in the future are shown graphically. [ABSTRACT FROM AUTHOR]

In the present investigations, we construct a new mathematical for the transmission dynamics of corona virus (COVID‐19) using the cases reported in Kingdom of Saudi Arabia for March 02 till July 31, 2020. We investigate the parameters values of the model using the least square curve fitting and the basic reproduction number is suggested for the given data is ℛ0 ≈ 1.2937. The stability results of the model are shown when the basic reproduction number is ℛ0 < 1. The model is locally asymptotically stable when ℛ0 < 1. Further, we show some important parameters that are more sensitive to the basic reproduction number ℛ0 using the PRCC method. The sensitive parameters that act as a control parameters that can reduce and control the infection in the population are shown graphically. The suggested control parameters can reduce dramatically the infection in the Kingdom of Saudi Arabia if the proper attention is paid to the suggested controls. [ABSTRACT FROM AUTHOR]

The virus that begins from Wuhan China, known as COVID-19 or coronavirus is still a huge panic for humans around the globe. The elimination of this virus from our society needs proper attentions to follows the rule suggested by World Health Organization (WHO). A vast literature on the modeling of this infection in various perspective is available. In the present work, we design a new mathematical model for COVID-19 pandemic by utilizing the real infected cases reported from Kingdom of Saudi Arabia. Initially, we formulate the model with the help of classical integer order nonlinear differential equations. The treatment class is considered the model to analyze the impact of treatment on the disease dynamics. The Caputo-Fabrizio derivative with the non-singular exponential kernel is applied in order to reformulate the proposed COVID-19 transmission model with a fractional order. The biologically important parameter called the basic reproductive number is investigated both theoretically and numerically. The estimated values of R 0 for the selected period are approximated to be 1.63. Further, by making use of the Picard Lindelöf theorem we provide the existence and uniqueness of the COVID-19 fractional epidemic model. Moreover, the fractional model is solved numerically and a number of simulation results are depicted using the real estimated parameters. The impact of various model parameters and memory index are shown graphically. We conclude that the fractional order epidemic models are more appropriate and provide deep insights into the disease dynamics. [ABSTRACT FROM AUTHOR]