Predicting and controlling the Ebola infection

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator

In this manuscript, we developed a nonlinear fractional order Ebola virus with a novel piecewise hybrid technique to observe the dynamical transmission having eight compartments. The existence and uniqueness of a solution of piecewise derivative is treated for a system with Arzel'a-Ascoli and Schauder conditions. We investigate the effects of classical and modified fractional calculus operators, specifically the classical Caputo piecewise operator, on the behavior of the model. A model shows that a completely continuous operator is uniformly continuous, and bounded according to the equilibrium points. The reproductive number R0 is derived for the biological feasibility of the model with sensitivity analysis with different parameters impact on the model. Sensitivity analysis is an essential tool for comprehending how various model parameters affect the spread of illness. Through a methodical manipulation of important parameters and an assessment of their impact on Ro, we are able to learn more about the resiliency and susceptibility of the model. Local stability is established with next Matignon method and global stability is conducted with the Lyapunov function for a feasible solution of the proposed model. In the end, a numerical solution is derived with Newton's polynomial technique for a piecewise Caputo operator through simulations of the compartments at various fractional orders by using real data. Our findings highlight the importance of fractional operators in enhancing the accuracy of the model in capturing the intricate dynamics of the disease. This research contributes to a deeper understanding of Ebola virus dynamics and provides valuable insights for improving disease modeling and public health strategies.

An innovative ensemble model based on deep learning for predicting COVID-19 infection

Nowadays, global public health crises are occurring more frequently, and accurate prediction of these diseases can reduce the burden on the healthcare system. Taking COVID-19 as an example, accurate prediction of infection can assist experts in effectively allocating medical resources and diagnosing diseases. Currently, scholars worldwide use single model approaches or epidemiology models more often to predict the outbreak trend of COVID-19, resulting in poor prediction accuracy. Although a few studies have employed ensemble models, there is still room for improvement in their performance. In addition, there are only a few models that use the laboratory results of patients to predict COVID-19 infection. To address these issues, research efforts should focus on improving disease prediction performance and expanding the use of medical disease prediction models. In this paper, we propose an innovative deep learning model Whale Optimization Convolutional Neural Networks (CNN), Long-Short Term Memory (LSTM) and Artificial Neural Network (ANN) called WOCLSA which incorporates three models ANN, CNN and LSTM. The WOCLSA model utilizes the Whale Optimization Algorithm to optimize the neuron number, dropout and batch size parameters in the integrated model of ANN, CNN and LSTM, thereby finding the global optimal solution parameters. WOCLSA employs 18 patient indicators as predictors, and compares its results with three other ensemble deep learning models. All models were validated with train-test split approaches. We evaluate and compare our proposed model and other models using accuracy, F1 score, recall, AUC and precision metrics. Through many studies and tests, our results show that our prediction models can identify patients with COVID-19 infection at the AUC of 91%, 91%, and 93% respectively. Other prediction results achieve a respectable accuracy of 92.82%, 92.79%, and 91.66% respectively, f1-score of 93.41%, 92.79%, and 92.33% respectively, precision of 93.41%, 92.79%, and 92.33% respectively, recall of 93.41%, 92.79%, and 92.33% respectively. All of these exceed 91%, surpassing those of comparable models. The execution time of WOCLSA is also an advantage. Therefore, the WOCLSA ensemble model can be used to assist in verifying laboratory research results and predict and to judge various diseases in public health events.

Epidemiological Analysis of Symmetry in Transmission of the Ebola Virus with Power Law Kernel

This study presents a mathematical model of non-integer order through the fractal fractional Caputo operator to determine the development of Ebola virus infections. To construct the model and conduct analysis, all Ebola virus cases are taken as incidence data. A symmetric approach is utilized for qualitative and quantitative analysis of the fractional order model. Additionally, stability is evaluated, along with the local and global effects of the virus that causes Ebola. Using the fractional order model of Ebola virus infections, the existence and uniqueness of solutions, as well the posedness and biological viability and disease free equilibrium points are confirmed. Many applications of fractional operators in modern mathematics exist, including the intricate and important study of symmetrical systems. Symmetry analysis is a powerful tool that enables the creation of numerical solutions for a given fractional differential equation very methodically. For this, we compare the results with the Caputo derivative operator to understand the dynamic behavior of the disease. The simulation demonstrates how all classes have convergent characteristics and maintain their places over time, reflecting the true behavior of Ebola virus infection. Power law kernel with the two step polynomial Newton method were used. This model seems to be quite strong and capable of reproducing the issue’s anticipated theoretical conditions.

Modelling the Role of Human Behaviour in Ebola Virus Disease (EVD) Transmission Dynamics

The role of human behaviour in the dynamics of infectious diseases cannot be underestimated. A clear understanding of how human behaviour influences the spread of infectious diseases is critical in establishing and designing control measures. To study the role that human behaviour plays in Ebola disease dynamics, in this paper, we design an Ebola virus disease model with disease transmission dynamics based on a new exponential nonlinear incidence function. This new incidence function that captures the reduction in disease transmission due to human behaviour innovatively considers the efficacy and the speed of behaviour change. The model's steady states are determined and suitable Lyapunov functions are built. The proofs of the global stability of equilibrium points are presented. To demonstrate the utility of the model, we fit the model to Ebola virus disease data from Liberia and Sierra Leone. The results which are comparable to existing findings from the outbreak of 2014 − 2016 show a better fit when the efficacy and the speed of behaviour change are higher. A rapid and efficacious behaviour change as a control measure to rapidly control an Ebola virus disease epidemic is advocated. Consequently, this model has implications for the management and control of future Ebola virus disease outbreaks.

An efficient spectral collocation method for the dynamic simulation of the fractional epidemiological model of the Ebola virus

This article investigates a family of approximate solutions for the fractional model (in the Liouville-Caputo sense) of the Ebola virus via an accurate numerical procedure (Chebyshev spectral collocation method). We reduce the proposed epidemiological model to a system of algebraic equations with the help of the properties of the Chebyshev polynomials of the third kind. Some theorems about the convergence analysis and the existence-uniqueness solution are stated. Finally, some numerical simulations are presented for different values of the fractional-order and the other parameters involved in the coefficients. We also note that we can apply the proposed method to solve other models.

Analytic solution of the SEIR epidemic model via asymptotic approximant

An analytic solution is obtained to the SEIR Epidemic Model. The solution is created by constructing a single second-order nonlinear differential equation in ln S and analytically continuing its divergent power series solution such that it matches the correct long-time exponential damping of the epidemic model. This is achieved through an asymptotic approximant (Barlow et al., 2017) in the form of a modified symmetric Padé approximant that incorporates this damping. The utility of the analytical form is demonstrated through its application to the COVID-19 pandemic.

Numerical Simulation of the Fractal-Fractional Ebola Virus

In this work we present three new models of the fractal-fractional Ebola virus. We investigate the numerical solutions of the fractal-fractional Ebola virus in the sense of three different kernels based on the power law, the exponential decay and the generalized Mittag-Leffler function by using the concepts of the fractal differentiation and fractional differentiation. These operators have two parameters: The first parameter ρ is considered as the fractal dimension and the second parameter k is the fractional order. We evaluate the numerical solutions of the fractal-fractional Ebola virus for these operators with the theory of fractional calculus and the help of the Lagrange polynomial functions. In the case of ρ=k=1, all of the numerical solutions based on the power kernel, the exponential kernel and the generalized Mittag-Leffler kernel are found to be close to each other and, therefore, one of the kernels is compared with such numerical methods as the finite difference methods. This has led to an excellent agreement. For the effect of fractal-fractional on the behavior, we study the numerical solutions for different values of ρ and k. All calculations in this work are accomplished by using the Mathematica package.

Analysis for fractional dynamics of Ebola virus model

Ebola virus is very challenging problem of the world. The main purpose of this work is to study fractional Ebola virus model. An efficient computational method based on iterative scheme is proposed to solve fractional Ebola model numerically. Stability of proposed method is also discussed. Efficiency of proposed method is shown by listing CPU time. Proposed computational method will work for long time domain. Numerical results are presented graphically. The main reason for using this technique is low computational cost and high accuracy. It is also shown how the approximate solution varies for fractional and integer order Ebola virus model.