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The SARS-CoV-2 virus pandemic remains a pressing issue with its unpredictable nature, and it spreads worldwide through human interaction. Current research focuses on the investigation and analysis of fractional epidemic models that discuss the temporal dynamics of the SARS-CoV-2 virus in the community. In this work, we choose a fractional-order mathematical model to examine the transmissibility in the community of several symptoms of COVID-19 in the sense of the Caputo operator. Sensitivity analysis of R0 and disease-free local stability of the system are checked. Also, with the assistance of fixed point theory, we demonstrate the existence and uniqueness of the system. In addition, numerically we solve the fractional model and presented some simulation results via actual estimation parameters. Graphically we displayed the effects of numerous model parameters and memory indexes. The numerical outcomes show the reliability, validation, and accuracy of the scheme. © 2022 the Author(s), licensee AIMS Press.
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In this study, the COVID-19 epidemic model is established by incorporating quarantine and isolation compartments with Mittag-Leffler kernel. The existence and uniqueness of the solutions for the proposed fractional model are obtained. The basic reproduction number, equilibrium points, and stability analysis of the COVID-19 model are derived. Sensitivity analysis is carried out to elaborate the influential parameters upon basic reproduction number. It is obtained that the disease transmission parameter is the most dominant parameter upon basic reproduction number. A convergent iterative scheme is taken into account to simulate the dynamical behavior of the system. We estimate the values of variables with the help of the least square curve fitting tool for the COVID-19 cases in Pakistan from 04 March to May 10, 2020, by using MATLAB.
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The fractional derivative is an advanced category of mathematics for real-life problems. This work focus on the investigation of 2nd wave of the Corona virus in India. We develop a time fractional order COVID-19 model with effects of the disease which consist of a system of fractional differential equations. The fractional-order COVID-19 model is investigated with AtanganaBaleanu-Caputo fractional derivative. Also, the deterministic mathematical model for the Omicron effect is investigated with different fractional parameters. The fractional-order system is analyzed qualitatively as well as verified sensitivity analysis. Fixed point theory is used to prove the existence and uniqueness of the fractional-order model. Analyzed the model locally as well as globally using Lyapunov first and second derivative. Boundedness and positive unique solutions are verified for the fractional-order model of infection of disease. The concept of fixed point theory is used to interrogate the problem and confine the solution. Solutions are derived to investigate the influence of fractional operator which shows the impact of the disease on society. Simulation has been made to understand the behavior of the virus.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).
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This current work presents an SEIQR model with fuzzy parameters. The use of fuzzy theory helps us to solve the problems of quantifying uncertainty in the mathematical modeling of diseases. The fuzzy reproduction number and fuzzy equilibrium points have been derived focusing on a model in a specific group of people having a triangular membership function. Moreover, a fuzzy non-standard finite difference (FNSFD) method for the model is developed. The stability of the proposed method is discussed in a fuzzy sense. A numerical verification for the proposed model is presented. The developed FNSFD scheme is a reliable method and preserves all the essential features of a continuous dynamical system.
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In this paper, we study a fractional order COVID-19 model using different techniques and analysis. The sumudu transform is applied with the environment as a route of infection in society to the proposed fractional-order model. It plays a significant part in issues of medical and engineering as well as its analysis in community. Initially, we present the model formation and its sensitivity analysis. Further, the uniqueness and stability analysis has been made for COVID-19 also used the iterative scheme with fixed point theorem. After using the Adams-Moulton rule to support our results, we examine some results using the fractal fractional operator. Demonstrate the numerical simulations to prove the efficiency of the given techniques. We illustrate the visual depiction of sensitive parameters that reveal the decrease and triumph over the virus within the network. We can reduce the virus by the appropriate recognition of the individuals in community of Saudi Arabia. © 2022 the Author(s), licensee AIMS Press.
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Objective: To evaluate the relationship between water use of countries and coronavirus disease-2019 (COVID-19) data in order to establish the effect of water dynamics on COVID-19 pandemics. Material and Methods: The country-based water consumption per capita (WC) and COVID-19 indices [total cases per 1 million population (CI-C) and deaths per 1 million population (CI-D)] collected from the Worldometer website and the Global Competitiveness Scores from The Global Competitiveness Report 2019 of World Economic Forum which was accessed at the day of May 30th, 2020. The relationship between water consumption and COVID-19 incidences was evaluated with “machine learning” methods. The statistical analyses were performed with the use of R software, version 4.0.0 (R Project for Statistical Computing). Results: For a total of 138 countries, we found a positive correlation between WC and CI-C (R 0.13). For the first 20 developed countries, we found a negative correlation between WC and CI-C and CI-D (R-0.18). The USA data is completely different from other 19 analyzed countries. The correlation coefficient becomes-0.44 when the USA is excluded, compared to-0.18 for all 20 countries including the USA. Conclusion: A negative relationship between water consumption and COVID-19 incidences was found at least for a relatively homogeneous group which is comprised of mainly developed countries. Among the developed countries, USA exhibits different characteristics. In contrast, when all 138 countries were analyzed, a positive relation was found. The results can be used from various disciplines since the water and its relations with micro-systems serve one of the most important issues for our present time and future.
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This paper derived fractional derivatives with Atangana-Baleanu, Atangana-Toufik scheme and fractal fractional Atangana-Baleanu sense for the COVID-19 model. These are advanced techniques that provide effective results to analyze the COVID-19 outbreak. Fixed point theory is used to derive the existence and uniqueness of the fractional-order model COVID-19 model. We also proved the property of boundedness and positivity for the fractional-order model. The Atangana-Baleanu technique and Fractal fractional operator are used with the Sumudu transform to find reliable results for fractional order COVID-19 Model. The generalized Mittag-Leffler law is also used to construct the solution with the different fractional operators. Numerical simulations are performed for the developed scheme in the range of fractional order values to explain the effects of COVID-19 at different fractional values and justify the theoretical outcomes, which will be helpful to understand the outbreak of COVID-19 and for control strategies. © 2022 the Author(s), licensee AIMS Press.
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COVID-19 acts as a serious challenge to the whole world. Epidemiological data of COVID-19 is collected through media and web sources to analyze and investigate a system of nonlinear ordinary differential equation to understand the outbreaks of this epidemic disease. We analyze the diseases free and endemic equilibrium point including stability of the model. The certain threshold value of the basic reproduction number R0 is found to observe whether population is in disease free state or endemic state. Moreover, the epidemic peak has been obtained and we expect a considerable number of cases. Finally, some numerical results are presented which show the effect of parameters estimation and different step size on our obtained solutions at the real data of some countries to check the actual behavior of the COVID-19 at different countries. © This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.