ABSTRACT
A mathematical model revealing the transmission mechanism of COVID-19 is produced and theoretically examined, which has helped us address the disease dynamics and treatment measures, such as vaccination for susceptible patients. The mathematical model containing the whole population was partitioned into six different compartments, represented by the SVEIQR model. Important properties of the model, such as the nonnegativity of solutions and their boundedness, are established. Furthermore, we calculated the basic reproduction number, which is an important parameter in infection models. The disease-free equilibrium solution of the model was determined to be locally and globally asymptotically stable. When the basic reproduction number (Formula presented.) is less than one, the disease-free equilibrium point is locally asymptotically stable. To discover the approximative solution to the model, a general numerical approach based on the Haar collocation technique was developed. Using some real data, the sensitivity analysis of (Formula presented.) was shown. We simulated the approximate results for various values of the quarantine and vaccination populations using Matlab to show the transmission dynamics of the Coronavirus-19 disease through graphs. The validation of the results by the Simulink software and numerical methods shows that our model and adopted methodology are appropriate and accurate and could be used for further predictions for COVID-19. © 2022 by the authors.
ABSTRACT
The SARS-CoV-2 pandemic is an urgent problem with unpredictable properties and is widespread worldwide through human interactions. This work aims to use Caputo-Fabrizio frac-tional operators to explore the complex action of the Covid-19 Omicron variant. A fixed-point the-orem and an iterative approach are used to prove the existence and singularity of the model's system of solutions. Laplace transform is used to generalize the fractional order model for stability and unique solution of the iterative scheme. A numerical scheme is also constructed by using an expo-nential law kernel for the computational and simulation of the Covid-19 Model. The graphs demon-strate that the fractional model of Covid-19 is accurate. In the sense of Caputo-Fabrizio, one can obtain trustworthy information about the model in either an integer or non-integer scenario. This sense also provides useful information about the model's complexity.(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-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
ABSTRACT
The current emergence of coronavirus (SARS-CoV-2 or COVID-19) has put the world in threat. Social distancing, quarantine and governmental measures such as lockdowns, social isolation, and public hygiene are helpful in fighting the pandemic, while awareness campaigns through social media (radio, TV, etc.) are essential for their implementation. On this basis, we propose and analyse a mathematical model for the dynamics of COVID-19 transmission influenced by awareness campaigns through social media. A time delay factor due to the reporting of the infected cases has been included in the model for making it more realistic. Existence of equilibria and their stability, and occurrence of Hopf bifurcation have been studied using qualitative theory. We have derived the basic reproduction number (R-0) which is dependent on the rate of awareness. We have successfully shown that public awareness has a significant role in controlling the pandemic. We have also seen that the time delay destabilizes the system when it crosses a critical value. In sum, this study shows that public awareness in the form of social distancing, lockdowns, testing, etc. can reduce the pandemic with a tolerable time delay.
ABSTRACT
In this paper, we develop the theory of fractional order hybrid differential equations involving Riemann-Liouville differential operators of order l is an element of (0, 1). We study the existence theory to a class of boundary value problems for fractional order hybrid differential equations. The sum of three operators is used to prove the key results for a couple of hybrid fixed point theorems. We obtain sufficient conditions for the existence and uniqueness of positive solutions. Moreover, examples are also presented to show the significance of the results.
ABSTRACT
In this article, we have considered nine countries where the epidemic shows steady state or has a rising trend and used the traditional SEIR model to estimate the parameter for COVID-19 disease. These parameters are contact rate, removal rate, basic reproduction number, initial doubling time, point of inflection, and epidemic rate. In another part of the work, we have considered five countries where the epidemic trend has not settled and used exponential smoothing technique to forecast the infected cases. The study reports a magnifiable concern for reducing the transmission rate in order to combat the disease. © 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
ABSTRACT
In this article, a brief biological structure and some basic properties of COVID-19 are described. A classical integer order model is modified and converted into a fractional order model with ξ as order of the fractional derivative. Moreover, a valued structure preserving the numerical design, coined as Grunwald–Letnikov non-standard finite difference scheme, is developed for the fractional COVID-19 model. Taking into account the importance of the positivity and boundedness of the state variables, some productive results have been proved to ensure these essential features. Stability of the model at a corona free and a corona existing equilibrium points is investigated on the basis of Eigen values. The Routh–Hurwitz criterion is applied for the local stability analysis. An appropriate example with fitted and estimated set of parametric values is presented for the simulations. Graphical solutions are displayed for the chosen values of ξ (fractional order of the derivatives). The role of quarantined policy is also determined gradually to highlight its significance and relevancy in controlling infectious diseases. In the end, outcomes of the study are presented. © 2022 Tech Science Press. All rights reserved.
ABSTRACT
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.
ABSTRACT
The aim is to explore a COVID-19 SEIR model involving Atangana-Baleanu Caputo type (ABC) fractional derivatives. Existence, uniqueness, positivity, and boundedness of the solutions for the alternative model are established. Some stability results of the proposed system are also presented. Numerical simulations results obtained in this paper, according to the real data, show that the model is more suitable for the disease evolution. © 2021. All Rights Reserved.
ABSTRACT
The citrus epidemic huanglongbing (HLB), allied with an uncultured bacterial pathogen, is blusterous the industry of citrus worldwide. In this research work, we analysed a fractional huanglongbing model to study the transmission dynamics of the disease. We considered Caputo and new generalized form of Caputo type fractional derivatives to solve the proposed HLB model using two different methods. We exemplified the all necessary graphical observations by the call of real numerical data to show the nature of the given model classes. The analysis regarding to existence of the solution are mentioned with the help of theorems. We observed that the given numerical techniques are strong and worked well to show the dynamics of the model against the time variable.
ABSTRACT
Novel coronavirus disease is a burning issue all over the world. Spreading of the novel coronavirus having the characteristic of rapid transmission whenever the air molecules or the freely existed virus includes in the surrounding and therefore the spread of virus follows a stochastic process instead of deterministic. We assume a stochastic model to investigate the transmission dynamics of the novel coronavirus. To do this, we formulate the model according to the charectersitics of the corona virus disease and then prove the existence as well as the uniqueness of the global positive solution to show the well posed-ness and feasibility of the problem. Following the theory of dynamical systems as well as by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions of the extinction and the existence of stationary distribution. Finally, we carry out the large scale numerical simulations to demonstrate the verification of our analytical results.