Stability and numerical analysis via non-standard finite difference scheme of a nonlinear classical and fractional order model.

In this paper, we develop a new mathematical model for an in-depth understanding of COVID-19 (Omicron variant). The mathematical study of an omicron variant of the corona virus is discussed. In this new Omicron model, we used idea of dividing infected compartment further into more classes i.e asymptomatic, symptomatic and Omicron infected compartment. Model is asymptotically locally stable whenever R0<1 and when R0≤1 at disease free equilibrium the system is globally asymptotically stable. Local stability is investigated with Jacobian matrix and with Lyapunov function global stability is analyzed. Moreover basic reduction number is calculated through next generation matrix and numerical analysis will be used to verify the model with real data. We consider also the this model under fractional order derivative. We use Grunwald-Letnikov concept to establish a numerical scheme. We use nonstandard finite difference (NSFD) scheme to simulate the results. Graphical presentations are given corresponding to classical and fractional order derivative. According to our graphical results for the model with numerical parameters, the population's risk of infection can be reduced by adhering to the WHO's suggestions, which include keeping social distances, wearing facemasks, washing one's hands, avoiding crowds, etc.

Mathematical analysis of COVID-19 by using SIR model with convex incidence rate.

This paper is about a new COVID-19 SIR model containing three classes; Susceptible S(t), Infected I(t), and Recovered R(t) with the Convex incidence rate. Firstly, we present the subject model in the form of differential equations. Secondly, "the disease-free and endemic equilibrium" is calculated for the model. Also, the basic reproduction number R 0 is derived for the model. Furthermore, the Global Stability is calculated using the Lyapunov Function construction, while the Local Stability is determined using the Jacobian matrix. The numerical simulation is calculated using the Non-Standard Finite Difference (NFDS) scheme. In the numerical simulation, we prove our model using the data from Pakistan. "Simulation" means how S(t), I(t), and R(t) protection, exposure, and death rates affect people with the elapse of time.

On nonlinear classical and fractional order dynamical system addressing COVID-19.

This work studies a new SEIR type mathematical model for SARS-CoV-2. We show how immigration, protection, death rate, exposure, cure rate and interaction of infected people with healthy people affect the population. Our model has four classes including susceptible, exposed, infected and recovered respectively. Here, we find the basic reproduction number and local stability through jacobean matrix. Lyapunov function theory is used to calculate the global stability for the problem under investigation. Also an attempt is made to derive some numerical interpretation under fractional derivative by using fractional order nonstandard finite difference (NSFD) sachem. The graphical presentations are given for some real data.

Global transmission dynamic of SIR model in the time of SARS-CoV-2.

This current work studies a new mathematical model for SARS-CoV-2. We show how immigration, protection, death rate, exposure, cure rate and interaction of infected people with healthy people affect the population. Our model is SIR model, which has three classes including susceptible, infected and recovered respectively. Here, we find the basic reproduction number and local stability through jacobean matrix. Lyapunvo function theory is used to calculate the global stability for the problem under investigation. Also a nonstandard finite difference sachem (NSFDS) is used to simulate the results.

A new fuzzy fractional order model of transmission of Covid-19 with quarantine class.

This paper is devoted to a study of the fuzzy fractional mathematical model reviewing the transmission dynamics of the infectious disease Covid-19. The proposed dynamical model consists of susceptible, exposed, symptomatic, asymptomatic, quarantine, hospitalized, and recovered compartments. In this study, we deal with the fuzzy fractional model defined in Caputo's sense. We show the positivity of state variables that all the state variables that represent different compartments of the model are positive. Using Gronwall inequality, we show that the solution of the model is bounded. Using the notion of the next-generation matrix, we find the basic reproduction number of the model. We demonstrate the local and global stability of the equilibrium point by using the concept of Castillo-Chavez and Lyapunov theory with the Lasalle invariant principle, respectively. We present the results that reveal the existence and uniqueness of the solution of the considered model through the fixed point theorem of Schauder and Banach. Using the fuzzy hybrid Laplace method, we acquire the approximate solution of the proposed model. The results are graphically presented via MATLAB-17.

Study of global dynamics of COVID-19 via a new mathematical model.

The theme of this paper focuses on the mathematical modeling and transmission mechanism of the new Coronavirus shortly noted as (COVID-19), endangering the lives of people and causing a great menace to the world recently. We used a new type epidemic model composed on four compartments that is susceptible, exposed, infected and recovered (SEIR), which describes the dynamics of COVID-19 under convex incidence rate. We simulate the results by using nonstandard finite difference method (NSFDS) which is a powerful numerical tool. We describe the new model on some random data and then by the available data of a particular regions of Subcontinents.