This work is the consideration of a fractal fractional mathematical model on the transmission and control of corona virus (COVID-19), in which the total population of an infected area is divided into susceptible, infected and recovered classes. We consider a fractal-fractional order
SIR
type model for investigation of Covid-19. To realize the transmission and control of corona virus in a much better way, first we study the stability of the corresponding deterministic model using next generation matrix along with basic reproduction number. After this, we study the qualitative analysis using "fixed point theory" approach. Next, we use fractional Adams-Bashforth approach for investigation of approximate solution to the considered model. At the end numerical simulation are been given by matlab to provide the validity of mathematical system having the arbitrary order and fractal dimension.
The dynamic of covid-19 epidemic model with a convex incidence rate is studied in this article. First, we formulate the model without control and study all the basic properties and results including local and global stability. We show the global stability of disease free equilibrium using the method of Lyapunov function theory while for disease endemic, we use the method of geometrical approach. Furthermore, we develop a model with suitable optimal control strategies. Our aim is to minimize the infection in the host population. In order to do this, we use two control variables. Moreover, sensitivity analysis complemented by simulations are performed to determine how changes in parameters affect the dynamical behavior of the system. Taking into account the central manifold theory the bifurcation analysis is also incorporated. The numerical simulations are performed in order to show the feasibility of the control strategy and effectiveness of the theoretical results.
In the present study, a nonlinear delayed coronavirus pandemic model is investigated in the human population. For study, we find the equilibria of susceptible-exposed-infected-quarantine-recovered model with delay term. The stability of the model is investigated using well-posedness, Routh Hurwitz criterion, Volterra Lyapunov function, and Lasalle invariance principle. The effect of the reproduction number on dynamics of disease is analyzed. If the reproduction number is less than one then the disease has been controlled. On the other hand, if the reproduction number is greater than one then the disease has become endemic in the population. The effect of the quarantine component on the reproduction number is also investigated. In the delayed analysis of the model, we investigated that transmission dynamics of the disease is dependent on delay terms which is also reflected in basic reproduction number. At the end, to depict the strength of the theoretical analysis of the model, computer simulations are presented.
Complex systems require rigorous analysis using effective method, in order to handle and interpret their information. Spectrum produced from Fourier transform infrared (FTIR) instrument is an example of a complex system, due to their overlapped bands and interactions within the spectrum. Thus, chemometrics techniques are required to further analyze the data, in particular, chemometrics fuzzy autocatalytic set (c-FACS). The c-FACS is initially used to analyze the FTIR spectra of gelatins. However, in this study, the c-FACS is generalized and implemented for analysis of Coronavirus disease 2019 (Covid-19), particularly, the pandemic outbreak in Malaysia. The daily Covid-19 cases in states in Malaysia are modeled and analyzed using c-FACS, to observe the trend and severity of the disease in Malaysia. As a result, the classification of severity of zones in Malaysia are identified. The obtained results offer descriptive insight for strategizing purposes in combating the Covid-19 outbreak in Malaysia.
The term COVID-19 is an abbreviation of Coronavirus 2019, which is considered a global pandemic that threatens the lives of millions of people. Early detection of the disease offers ample opportunity of recovery and prevention of spreading. This paper proposes a method for classification and early detection of COVID-19 through image processing using X-ray images. A set of procedures are applied, including preprocessing (image noise removal, image thresholding, and morphological operation), Region of Interest (ROI) detection and segmentation, feature extraction, (Local binary pattern (LBP), Histogram of Gradient (HOG), and Haralick texture features) and classification (K-Nearest Neighbor (KNN) and Support Vector Machine (SVM)). The combinations of the feature extraction operators and classifiers results in six models, namely LBP-KNN, HOG-KNN, Haralick-KNN, LBP-SVM, HOG-SVM, and Haralick-SVM. The six models are tested based on test samples of 5,000 images with the percentage of training of 5-folds cross-validation. The evaluation results show high diagnosis accuracy from 89.2% up to 98.66%. The LBP-KNN model outperforms the other models in which it achieves an average accuracy of 98.66%, a sensitivity of 97.76%, specificity of 100%, and precision of 100%. The proposed method for early detection and classification of COVID-19 through image processing using X-ray images is proven to be usable in which it provides an end-to-end structure without the need for manual feature extraction and manual selection methods.
In 2019, a new infectious disease called pandemic COVID-19 began to spread from Wuhan, China. In spite of the efforts to stop the disease, being out of the control of the governments it spread rapidly all over the world. From then on, much research has been done in the world with the aim of controlling this contagious disease. A mathematical model for modeling the spread of COVID-19 and also controlling the spread of the disease has been presented in this paper. We find the disease-free equilibrium points as trivial equilibrium (TE), virus absenteeism equilibrium (VAE) and virus incidence equilibrium (VIE) for the proposed model; and at the trivial equilibrium point for the presented dynamic system we obtain the Jacobian matrix so as to be used in finding the largest eigenvalue. Radius spectral method has been used for finding the reproductive number. In the following, by adding a controller to the model and also using the theory of optimal control, we can improve the performance of the model. We must have a correct understanding of the system i.e. how it works, the various variables affecting the system, and the interaction of the variables on each other. To search for the optimal values, we need to use an appropriate optimization method. Given the limitations and needs of the problem, the aim of the optimization is to find the best solutions, to find conditions that result in the maximum of susceptiblity, the minimum of infection, and optimal quarantination.
This article focus the elimination and control of the infection caused by COVID-19. Mathematical model of the disease is formulated. With help of sensitivity analysis of the reproduction number the most sensitive parameters regarding transmission of infection are found. Consequently strategies for the control of infection are proposed. Threshold condition for global stability of the disease free state is investigated. Finally, using Matlab numerical simulations are produced for validation of theocratical results.
The outburst of the pandemic Coronavirus disease since December 2019, has severely impacted the health and economy worldwide. The epidemic is spreading fast through various means, as the virus is very infectious. Medical science is exploring a vaccine, only symptomatic treatment is possible at the moment. To contain the virus, it is required to categorize the risk factors and rank those in terms of contagion. This study aims to evaluate risk factors involved in the spread of COVID-19 and to rank them. In this work, we applied the methodology namely, Fuzzy Analytic Hierarchy Process (FAHP) to find out the weights and finally Hesitant Fuzzy Sets (HFS) with Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is applied to identify the major risk factor. The results showed that "long duration of contact with the infected person" the most significant risk factor, followed by "spread through hospitals and clinic" and "verbal spread". We showed the appliance of the Multi Criteria Decision Making (MCDM) tools in evaluation of the most significant risk factor. Moreover, we conducted sensitivity analysis.
Coronavirus is a pandemic that has become a concern for the whole world. This disease has stepped out to its greatest extent and is expanding day by day. Coronavirus, termed as a worldwide disease, has caused more than 8 lakh deaths worldwide. The foremost cause of the spread of coronavirus is SARS-CoV and SARS-CoV-2, which are part of the coronavirus family. Thus, predicting the patients suffering from such pandemic diseases would help to formulate the difference in inaccurate and infeasible time duration. This paper mainly focuses on the prediction of SARS-CoV and SARS-CoV-2 using the B-cells dataset. The paper also proposes different ensemble learning strategies that came out to be beneficial while making predictions. The predictions are made using various machine learning models. The numerous machine learning models, such as SVM, Naïve Bayes, K-nearest neighbors, AdaBoost, Gradient boosting, XGBoost, Random forest, ensembles, and neural networks are used in predicting and analyzing the dataset. The most accurate result was obtained using the proposed algorithm with 0.919 AUC score and 87.248% validation accuracy for predicting SARS-CoV and 0.923 AUC and 87.7934% validation accuracy for predicting SARS-CoV-2 virus.
In present time, the whole world is in the phase of war against the deadly pandemic COVID'19 and working on different interventions in this regard. Variety of strategies are taken into account from ground level to the state to reduce the transmission rate. For this purpose, the epidemiologists are also augmenting their contribution in structuring such models that could depict a scheme to diminish the basic reproduction number. These tactics also include the awareness campaigns initiated by the stakeholders through digital, print media and etc. Analyzing the cost and profit effectiveness of these tactics, we design an optimal control dynamical model to study the proficiency of each strategy in reducing the virulence of COVID'19. The aim is to illustrate the memory effect on the dynamics of COVID'19 with and without prevention measures through fractional calculus. Therefore, the structure of the model is in line with generalized proportional fractional derivative to assess the effects at each chronological change. Awareness about using medical mask, social distancing, frequent use of sanitizer or cleaning hand and supportive care during treatment are the strategies followed worldwide in this fight. Taking these into consideration, the optimal objective function proposed for the surveillance mitigation of COVID'19, is contemplated as the cost function. The effect analysis is supported through graphs and tabulated values. In addition, sensitivity inspection of basic reproduction number is also carried out with respect to different values of fractional index and cost function. Ultimately, social distancing and supportive care of infected are found to be significant in decreasing the basic reproduction number more rapidly.
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.
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.