On fractal-fractional Covid-19 mathematical model

The role of a vaccine booster for a fractional order model of the dynamic of COVID-19: a case study in Thailand

This article addresses the critical need for understanding the dynamics of COVID-19 transmission and the role of booster vaccinations in managing the pandemic. Despite widespread vaccination efforts, the emergence of new variants and the waning of immunity over time necessitate more effective strategies. A fractional-order mathematical model using Caputo-Fabrizio derivatives was developed to analyze the impact of booster doses, symptomatic and asymptomatic infections, and quarantine measures. The model incorporates real epidemic data from Thailand and includes a sensitivity analysis of parameters influencing disease spread. Numerical results indicate that booster vaccinations significantly reduce transmission rates, and the model's predictions align well with the observed data. The basic reproduction number was determined to evaluate disease control, showing that a sustained vaccination campaign, including booster doses, is essential to maintaining immunity and controlling future outbreaks. The findings underscore the importance of ongoing vaccination efforts and provide a robust framework for policymakers to design effective strategies for pandemic control.

Analysis of age wise fractional order problems for the Covid-19 under non-singular kernel of Mittag-Leffler law

The developed article considers SIR problems for the recent COVID-19 pandemic, in which each component is divided into two subgroups: young and adults. These subgroups are distributed among two classes in each compartment, and the effect of COVID-19 is observed in each class. The fractional problem is investigated using the non-singular operator of Atangana Baleanu in the Caputo sense (ABC). The existence and uniqueness of the solution are calculated using the fundamental theorems of fixed point theory. The stability development is also determined using the Ulam-Hyers stability technique. The approximate solution is evaluated using the fractional Adams-Bashforth technique, providing a wide range of choices for selecting fractional order parameters. The simulation is plotted against available data to verify the obtained scheme. Different fractional-order approximations are compared to integer-order curves of various orders. Therefore, this analysis represents the recent COVID-19 pandemic, differentiated by age at different fractional orders. The analysis reveals the impact of COVID-19 on young and adult populations. Adults, who typically have weaker immune systems, are more susceptible to infection compared to young people. Similarly, recovery from infection is higher among young infected individuals compared to infected cases in adults.

A bifurcation analysis and model of Covid-19 transmission dynamics with post-vaccination infection impact

SARS COV-2 (Covid-19) has imposed a monumental socio-economic burden worldwide, and its impact still lingers. We propose a deterministic model to describe the transmission dynamics of Covid-19, emphasizing the effects of vaccination on the prevailing epidemic. The proposed model incorporates current information on Covid-19, such as reinfection, waning of immunity derived from the vaccine, and infectiousness of the pre-symptomatic individuals into the disease dynamics. Moreover, the model analysis reveals that it exhibits the phenomenon of backward bifurcation, thus suggesting that driving the model reproduction number below unity may not suffice to drive the epidemic toward extinction. The model is fitted to real-life data to estimate values for some of the unknown parameters. In addition, the model epidemic threshold and equilibria are determined while the criteria for the stability of each equilibrium solution are established using the Metzler approach. A sensitivity analysis of the model is performed based on the Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCCs) approaches to illustrate the impact of the various model parameters and explore the dependency of control reproduction number on its constituents parameters, which invariably gives insight on what needs to be done to contain the pandemic effectively. The foregoing notwithstanding, the contour plots of the control reproduction number concerning some of the salient parameters indicate that increasing vaccination coverage and decreasing vaccine waning rate would remarkably reduce the value of the reproduction number below unity, thus facilitating the possible elimination of the disease from the population. Finally, the model is solved numerically and simulated for different scenarios of disease outbreaks with the findings discussed.

Mathematical analysis of stochastic epidemic model of MERS-corona & application of ergodic theory

The "Middle East Respiratory" (MERS-Cov) is among the world's dangerous diseases that still exist. Presently it is a threat to Arab countries, but it is a horrible prediction that it may propagate like COVID-19. In this article, a stochastic version of the epidemic model, MERS-Cov, is presented. Initially, a mathematical form is given to the dynamics of the disease while incorporating some unpredictable factors. The study of the underlying model shows the existence of positive global solution. Formulating appropriate Lyapunov functionals, the paper will also explore parametric conditions which will lead to the extinction of the disease from a community. Moreover, to reveal that the infection will persist, ergodic stationary distribution will be carried out. It will also be shown that a threshold quantity exists, which will determine some essential parameters for exploring other dynamical aspects of the main model. With the addition of some examples, the underlying stochastic model of MERS-Cov will be studied graphically for more illustration.

Reduction of fluid forces for flow past side-by-side cylinders using downstream attached splitter plates

A two-dimensional numerical simulation is performed to investigate the drag reduction and vortex shedding suppression behind three square cylinders with attached splitter plates in the downstream region at a low Reynolds number (Re = 150). Numerical calculations are carried out using the lattice Boltzmann method. The study is carried out for various values of gap spacing between the cylinders and different splitter plate lengths. The vortices are completely chaotic at very small spacing, as observed. The splitter plates are critical in suppressing shedding and reducing drag on the objects. The splitter plates with lengths greater than two fully control the jet interaction at low spacing values. There is maximum percentage reduction in CDmean for small spacing and the selected largest splitter plate length. Furthermore, systematic investigation reveals that splitter plates significantly suppress the fluctuating lift in addition to drastically reducing the drag.

Reactive-diffusion epidemic model on human mobility networks: Analysis and applications to COVID-19 in China

The complex dynamics of human mobility, combined with sporadic cases of local outbreaks, make assessing the impact of large-scale social distancing on COVID-19 propagation in China a challenge. In this paper, with the travel big dataset supported by Baidu migration platform, we develop a reactive-diffusion epidemic model on human mobility networks to characterize the spatio-temporal propagation of COVID-19, and a novel time-dependent function is incorporated into the model to describe the effects of human intervention. By applying the system control theory, we discuss both constant and time-varying threshold behavior of proposed model. In the context of population mobility-mediated epidemics in China, we explore the transmission patterns of COVID-19 in city clusters. The results suggest that human intervention significantly inhibits the high correlation between population mobility and infection cases. Furthermore, by simulating different population flow scenarios, we reveal spatial diffusion phenomenon of cases from cities with high infection density to cities with low infection density. Finally, our model exhibits acceptable prediction performance using actual case data. The localized analytical results verify the ability of the PDE model to correctly describe the epidemic propagation and provide new insights for controlling the spread of COVID-19.

Fractional model analysis of COVID-19 spread based on big data platform

Based on the data of COVID-19, this paper establishes the FCSEIR model for the spread through data analysis and designs the related simulation software. Using the data from Shanghai, the spread of the virus was simulated and predicted, and the process from outbreak to control of this infectious disease was better analyzed.

A New Fractal-Fractional Version of Giving up Smoking Model: Application of Lagrangian Piece-Wise Interpolation along with Asymptotical Stability

In this paper, a new kind of mathematical modeling is studied by providing a five-compartmental system of differential equations with respect to new hybrid generalized fractal-fractional derivatives. For the first time, we design a model of giving up smoking to analyze its dynamical behaviors by considering two parameters of such generalized operators; i.e., fractal dimension and fractional order. We apply a special sub-category of increasing functions to investigate the existence of solutions. Uniqueness property is derived by a standard method based on the Lipschitz rule. After proving stability property, the equilibrium points are obtained and asymptotically stable solutions are studied. Finally, we illustrate all analytical results and findings via numerical algorithms and graphs obtained by Lagrangian piece-wise interpolation, and discuss all behaviors of the relevant solutions in the fractal-fractional system.

Remarks on Fractal-Fractional Malkus Waterwheel Model with Computational Analysis

In this paper, we investigate the fractal-fractional Malkus Waterwheel model in detail. We discuss the existence and uniqueness of a solution of the fractal-fractional model using the fixed point technique. We apply a very effective method to obtain the solutions of the model. We prove with numerical simulations the accuracy of the proposed method. We put in evidence the effects of the fractional order and the fractal dimension for a symmetric Malkus Waterwheel model.

Caputo Fractal Fractional Order Derivative of Soil Pollution Model Due to Industrial and Agrochemical

This paper narrates a non-linear and non-local Caputo fractal fractional operator of eco epidemic model with the advance of soil pollution considered in five compartments. The qualitative analysis of solutions such as existence and uniqueness of the model is carried out by using the standard condition of Schauder's fixed point theorem and Banach Contraction principle. The local and global stability are characterized with the help of basic reproduction number. The Ulam-Hyer stability is analyzed for the small perturbation. The Power law kernel is used to get a reliable result for the soil pollution model. Analytical solution studied by means of Modified Euler method. Numerical simulation of Euler scheme algorithm is performed to show the effects of various fractional orders ( 0.5 < η < 1 ) and validating the theoretical parameter values of real time data by the support of MATLAB.

A fractal fractional order vaccination model of COVID-19 pandemic using Adam’s moulton analysis

The pandemic caused by coronaviruses (SARS-COV-2) is a zoonotic disease targeting the respiratory tract of active humans. Few mild symptoms of fever and tiredness get cured without any medicinal aid, whereas some severe symptoms of dry cough with breathing illness led to perceived risk of secondary transmission. This paper studies the effectiveness of vaccination in Covid-19​ pandemic disease by modelling three compartments susceptible, vaccinated and infected (SVI) of Atangana Baleanu of Caputo (ABC) type derivatives in non-integer order. The disease dynamics is analysed and its stability is performed. Numerical approximation is derived using Adam’s Moulton method and simulated to forecast the results for controllability of pandemic spread.

Dynamical Behavior of a Fractional Order Model for Within-Host SARS-CoV-2

The prime objective of the current study is to propose a novel mathematical framework under the fractional-order derivative, which describes the complex within-host behavior of SARS-CoV-2 by taking into account the effects of memory and carrier. To do this, we formulate a mathematical model of SARS-CoV-2 under the Caputo fractional-order derivative. We derived the conditions for the existence of equilibria of the model and computed the basic reproduction number R0. We used mathematical analysis to establish the proposed model’s local and global stability results. Some numerical resolutions of our theoretical results are presented. The main result of this study is that as the fractional derivative order increases, the approach of the solution to the equilibrium points becomes faster. It is also observed that the value of R0 increases as the value of β and πv increases.

Global Stability of a Humoral Immunity COVID-19 Model with Logistic Growth and Delays

The mathematical modeling and analysis of within-host or between-host coronavirus disease 2019 (COVID-19) dynamics are considered robust tools to support scientific research. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the cause of COVID-19. This paper proposes and investigates a within-host COVID-19 dynamics model with latent infection, the logistic growth of healthy epithelial cells and the humoral (antibody) immune response. Time delays can affect the dynamics of SARS-CoV-2 infection predicted by mathematical models. Therefore, we incorporate four time delays into the model: (i) delay in the formation of latent infected epithelial cells, (ii) delay in the formation of active infected epithelial cells, (iii) delay in the activation of latent infected epithelial cells, and (iv) maturation delay of new SARS-CoV-2 particles. We establish that the model’s solutions are non-negative and ultimately bounded. This confirms that the concentrations of the virus and cells should not become negative or unbounded. We deduce that the model has three steady states and their existence and stability are perfectly determined by two threshold parameters. We use Lyapunov functionals to confirm the global stability of the model’s steady states. The analytical results are enhanced by numerical simulations. The effect of time delays on the SARS-CoV-2 dynamics is investigated. We observe that increasing time delay values can have the same impact as drug therapies in suppressing viral progression. This offers some insight useful to develop a new class of treatment that causes an increase in the delay periods and then may control SARS-CoV-2 replication.