Fractional order mathematical modeling of novel corona virus (COVID-19)

Understanding zoonotic disease spread with a fractional order epidemic model

Zoonotic diseases, which are transmitted between animals and humans, pose significant public health challenges, especially in regions with high human-wildlife interactions. This study presents a novel fractional-order mathematical model to analyze the transmission dynamics of zoonotic diseases between baboons and humans in the Al-Baha region. The model incorporates the Atangana-Baleanu fractional derivative to account for memory effects and spatial heterogeneity, offering a more realistic representation of disease spread. The fractional Euler method is employed for numerical simulations, enabling accurate predictions of infection trends under various fractional orders. Stability analysis, conducted via the Banach fixed-point theorem and Picard iterative method, confirms the model's robustness, while Hyers-Ulam stability ensures its reliability. Additionally, control strategies, including sterilization, food access restriction, and human interaction reduction, are integrated into the model to assess their effectiveness in disease mitigation. Simulation results highlight the impact of fractional-rder dynamics on disease persistence, showing that lower fractional orders correspond to prolonged infections due to memory effects. These findings underscore the significance of fractional calculus in epidemiological modeling and provide valuable insights for designing effective zoonotic disease control strategies.

Dynamics of infectious disease mathematical model through unsupervised stochastic neural network paradigm

The viruses has spread globally and have been impacted lives of people socially and economically, which causes immense suffering throughout the world. Thousands of people died and millions of illnesses were brought, by the outbreak worldwide. In order to control the coronavirus pandemic, mathematical modeling proved to be an invaluable tool for analyzing and determining the potential and severity of the illness. This work proposed and assessed a deterministic six-compartment model with a novel stochastic neural network. The significance of the proposed model was demonstrated by numerical simulation in which the results are agreed with sensitivity analysis. Furthermore, the efficacy of stochastic neural network has been proven with the help of numerical simulations. Some investigations have been conducted through graphs and tables that how the vaccination process is helpful to minimize stress in society. The numerical simulations also focused on preventing the community-wide spread of the disease. The lowest residual errors have been achieved by our proposed stochastic neural network and compared with numerical solvers to assess the accuracy and robustness of the proposed approach.

COVID-19 risk perceptions in Japan: a cross-sectional study

We conducted a large-scale online survey in February 2023 to investigate the public's perceptions of COVID-19 infection and fatality risks in Japan. We identified two key findings. First, univariate analysis comparing perceived and actual risk suggested overestimation and nonnegligible underestimation of COVID-19 risk. Second, multivariate logistic regression analyses revealed that age, income, education levels, health status, information sources, and experiences related to COVID-19 were associated with risk perceptions. Given that risk perceptions are closely correlated with daily socioeconomic activities and well-being, it is important for policy-makers and public health experts to understand how to communicate COVID-19 risk to the public effectively.

Application of a time-fractal fractional derivative with a power-law kernel to the Burke-Shaw system based on Newton's interpolation polynomials

This paper proposes some updated and improved numerical schemes based on Newton's interpolation polynomial. A Burke-Shaw system of the time-fractal fractional derivative with a power-law kernel is presented as well as some illustrative examples. To solve the model system, the fractal-fractional derivative operator is used. Under Caputo's fractal-fractional operator, fixed point theory proves Burke-Shaw's existence and uniqueness. Additionally, we have calculated the Lyapunov exponent (LE) of the proposed system. This method is illustrated with a numerical example to demonstrate the applicability and efficiency of the suggested method. To analyze this system numerically, we use a fractal- fractional numerical scheme with a power-law kernel to analyze the variable order fractal- fractional system. Furthermore, the Atangana-Seda numerical scheme, based on Newton polynomials, has been used to solve this problem. This novel method is illustrated with numerical examples. Simulated and analytical results agree. We contribute to real-world mathematical applications. Finally, we applied a numerical successive approximation method to solve the fractional model.•The purpose of this section is to define a mathematical model to study the dynamic behavior of the Burke-Shaw system.•With the Danca algorithm [1,2] and Adams-Bashforth-Moulton numerical scheme, we compute the Lyapunov exponent of the system, which is useful for studying Dissipativity.•In a generalized numerical method, we simulate the solutions of the system using the time-fractal fractional derivative of Atangana-Seda.

A case study of 2019-nCoV in Russia using integer and fractional order derivatives

In this article, we define a mathematical model to analyze the outbreaks of the most deadly disease of the decade named 2019-nCoV by using integer and fractional order derivatives. For the case study, the real data of Russia is taken to perform novel parameter estimation by using the Trust Region Reflective (TRR) algorithm. First, we define an integer order model and then generalize it by using fractional derivatives. A novel optimal control problem is derived to see the impact of possible preventive measures against the spread of 2019-nCoV. We implement the forward-backward sweep method to numerically solve our proposed model and control problem. A number of graphs have been plotted to see the impact of the proposed control practically. The Russian data-based parameter estimation along with the proposal of a mathematical model in the sense of Caputo fractional derivative that contains the memory term in the system are the main novel features of this study.

Study of Fractional Order SEIR Epidemic Model and Effect of Vaccination on the Spread of COVID-19

In this manuscript, a fractional order SEIR model with vaccination has been proposed. The positivity and boundedness of the solutions have been verified. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium point E 0 when R 0 < 1 and at epidemic equilibrium E 1 whenR 0 > 1 . It has been found that introduction of the vaccination parameter η reduces the reproduction number R 0 . The parameters are identified using real-time data from COVID-19 cases in India. To numerically solve the SEIR model with vaccination, the Adam-Bashforth-Moulton technique is used. We employed MATLAB Software (Version 2018a) for graphical presentations and numerical simulations.. It has been observed that the SEIR model with fractional order derivatives of the dynamical variables is much more effective in studying the effect of vaccination than the integral model.

Modeling the dynamics of COVID-19 using fractal-fractional operator with a case study

This research study consists of a newly proposed Atangana-Baleanu derivative for transmission dynamics of the coronavirus (COVID-19) epidemic. Taking the advantage of non-local Atangana-Baleanu fractional-derivative approach, the dynamics of the well-known COVID-19 have been examined and analyzed with the induction of various infection phases and multiple routes of transmissions. For this purpose, an attempt is made to present a novel approach that initially formulates the proposed model using classical integer-order differential equations, followed by application of the fractal fractional derivative for obtaining the fractional COVID-19 model having arbitrary order Ψ and the fractal dimension Ξ . With this motive, some basic properties of the model that include equilibria and reproduction number are presented as well. Then, the stability of the equilibrium points is examined. Furthermore, a novel numerical method is introduced based on Adams-Bashforth fractal-fractional approach for the derivation of an iterative scheme of the fractal-fractional ABC model. This in turns, has helped us to obtained detailed graphical representation for several values of fractional and fractal orders Ψ and Ξ , respectively. In the end, graphical results and numerical simulation are presented for comprehending the impacts of the different model parameters and fractional order on the disease dynamics and the control. The outcomes of this research would provide strong theoretical insights for understanding mechanism of the infectious diseases and help the worldwide practitioners in adopting controlling strategies.

A mathematical study on a fractional COVID-19 transmission model within the framework of nonsingular and nonlocal kernel

In this work, a mathematical model consisting of a compartmentalized coupled nonlinear system of fractional order differential equations describing the transmission dynamics of COVID-19 is studied. The fractional derivative is taken in the Atangana-Baleanu-Caputo sense. The basic dynamic properties of the fractional model such as invariant region, existence of equilibrium points as well as basic reproduction number are briefly discussed. Qualitative results on the existence and uniqueness of solutions via a fixed point argument as well as stability of the model solutions in the sense of Ulam-Hyers are furnished. Furthermore, the model is fitted to the COVID-19 data circulated by Nigeria Centre for Disease Control and the two-step Adams-Bashforth method incorporating the noninteger order parameter is used to obtain an iterative scheme from which numerical results for the model can be generated. Numerical simulations for the proposed model using Adams-Bashforth iterative scheme are presented to describe the behaviors at distinct values of the fractional index parameter for of each of the system state variables. It was shown numerically that the value of fractional index parameter has a significant effect on the transmission behavior of the disease however, the infected population (the exposed, the asymptomatic infectious, the symptomatic infectious) shrinks with time when the basic reproduction number is less than one irrespective of the value of fractional index parameter.

Investigation of fractal-fractional order model of COVID-19 in Pakistan under Atangana-Baleanu Caputo (ABC) derivative

This manuscript addressing the dynamics of fractal-fractional type modified SEIR model under Atangana-Baleanu Caputo (ABC) derivative of fractional order y and fractal dimension p for the available data in Pakistan. The proposed model has been investigated for qualitative analysis by applying the theory of non-linear functional analysis along with fixed point theory. The fractional Adams-bashforth iterative techniques have been applied for the numerical solution of the said model. The Ulam-Hyers (UH) stability techniques have been derived for the stability of the considered model. The simulation of all compartments has been drawn against the available data of covid-19 in Pakistan. The whole study of this manuscript illustrates that control of the effective transmission rate is necessary for stoping the transmission of the outbreak. This means that everyone in the society must change their behavior towards self-protection by keeping most of the precautionary measures sufficient for controlling covid-19.