Stability and numerical analysis via non-standard finite difference scheme of a nonlinear classical and fractional order model.

In this paper, we develop a new mathematical model for an in-depth understanding of COVID-19 (Omicron variant). The mathematical study of an omicron variant of the corona virus is discussed. In this new Omicron model, we used idea of dividing infected compartment further into more classes i.e asymptomatic, symptomatic and Omicron infected compartment. Model is asymptotically locally stable whenever R0<1 and when R0≤1 at disease free equilibrium the system is globally asymptotically stable. Local stability is investigated with Jacobian matrix and with Lyapunov function global stability is analyzed. Moreover basic reduction number is calculated through next generation matrix and numerical analysis will be used to verify the model with real data. We consider also the this model under fractional order derivative. We use Grunwald-Letnikov concept to establish a numerical scheme. We use nonstandard finite difference (NSFD) scheme to simulate the results. Graphical presentations are given corresponding to classical and fractional order derivative. According to our graphical results for the model with numerical parameters, the population's risk of infection can be reduced by adhering to the WHO's suggestions, which include keeping social distances, wearing facemasks, washing one's hands, avoiding crowds, etc.

Exploring undergraduate students' attitudes towards emergency online learning during COVID-19: A case from the UAE

This qualitative study aims to investigate the attitudes of undergraduate students towards their experience with emergency online learning during the first few weeks of the mandatory shift to online learning caused by COVID-19. Students from two general English courses at a university located in Abu Dhabi in United Arab Emirates were asked to write semi-guided essays during the week preceding the final exams of the second semester of the academic year 2019–20. A sample of these essays was analyzed using open coding. Findings revealed that cost- and time-effectiveness, safety, convenience and improved participation were the most frequently cited positive aspects of the emergency online learning experience, while distraction and reduced focus, heavy workload, problems with technology and the internet, and insufficient support from instructors and colleagues were the most recurrent negative aspects. The findings of the study help instructors and institutions understand students' attitudes regarding online learning under abnormal circumstances. A number of recommendations informed by the interpretation of the participants' feedback are offered to assist instructors, administrators and policy makers improve future online learning experiences.

The investigation of energy management and atomic interaction between coronavirus structure in the vicinity of aqueous environment of H2O molecules via molecular dynamics approach.

The coronavirus pandemic is caused by intense acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Identifying the atomic structure of this virus can lead to the treatment of related diseases in medical cases. In the current computational study, the atomic evolution of the coronavirus in an aqueous environment using the Molecular Dynamics (MD) approach is explained. The virus behaviors by reporting the physical attributes such as total energy, temperature, potential energy, interaction energy, volume, entropy, and radius of gyration of the modeled virus are reported. The MD results indicated the atomic stability of the simulated virus significantly reduced after 25.33 ns. Furthermore, the volume of simulated virus changes from 182397 Å3 to 372589 Å3 after t = 30 ns. This result shows the atomic interaction between various atoms in coronavirus structure decreases in the vicinity of H2O molecules. Numerically, the interaction energy between virus and aqueous environment converges to -12387 eV and -251 eV values in the initial and final time steps of the MD study procedure, respectively.

COVID-19 Infected Lung Computed Tomography Segmentation and Supervised Classification Approach

The purpose of this research is the segmentation of lungs computed tomography (CT) scan for the diagnosis of COVID-19 by using machine learning methods. Our dataset contains data from patients who are prone to the epidemic. It contains three types of lungs CT images (Normal, Pneumonia, and COVID-19) collected from two different sources;the first one is the Radiology Department of Nishtar Hospital Multan and Civil Hospital Bahawalpur, Pakistan, and the second one is a publicly free available medical imaging database known as Radiopaedia. For the preprocessing, a novel fuzzy c-mean automated region-growing segmentation approach is deployed to take an automated region of interest (ROIs) and acquire 52 hybrid statistical features for each ROIs. Also, 12 optimized statistical features are selected via the chi-square feature reduction technique. For the classification, five machine learning classifiers named as deep learning J4, multilayer perceptron, support vector machine, random forest, and naive Bayes are deployed to optimize the hybrid statistical features dataset. It is observed that the deep learning J4 has promising results (sensitivity and specificity: 0.987;accuracy: 98.67%) among all the deployed classifiers. As a complementary study, a statistical work is devoted to the use of a new statistical model to fit the main datasets of COVID-19 collected in Pakistan.

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.

Dynamical analysis of fractional-order tobacco smoking model containing snuffing class

The cur­rent pan­demic sit­u­a­tion caused by COVID-19 has affected human life globally at the economic, social and men­tal health levels. Specifically, ten­sion has led an in­creas­ing number of people to the consumption of various types of to­bacco.. In this work, an existing tobacco smoking model with a specific class of tobacco snuffing is converted into a fractional order as many applications of fractional derivatives to recall the past history of smokers in the present model. For this purpose, we use fractional derivative in Caputo sense to study the model in the form of fractional order. Then Positivity, boundness and dynamics of the proposed model are investigated. For numerical results, the generalized “Adams–Bashforth–Moulton Method (GABMM) and fourth-order Runge–Kutta (RK4) method” are used to solve the proposed model and Matlab numerical computing environment is the current software used.

A fractional order mathematical model for COVID-19 dynamics with quarantine, isolation, and environmental viral load.

COVID-19 or coronavirus is a newly emerged infectious disease that started in Wuhan, China, in December 2019 and spread worldwide very quickly. Although the recovery rate is greater than the death rate, the COVID-19 infection is becoming very harmful for the human community and causing financial loses to their economy. No proper vaccine for this infection has been introduced in the market in order to treat the infected people. Various approaches have been implemented recently to study the dynamics of this novel infection. Mathematical models are one of the effective tools in this regard to understand the transmission patterns of COVID-19. In the present paper, we formulate a fractional epidemic model in the Caputo sense with the consideration of quarantine, isolation, and environmental impacts to examine the dynamics of the COVID-19 outbreak. The fractional models are quite useful for understanding better the disease epidemics as well as capture the memory and nonlocality effects. First, we construct the model in ordinary differential equations and further consider the Caputo operator to formulate its fractional derivative. We present some of the necessary mathematical analysis for the fractional model. Furthermore, the model is fitted to the reported cases in Pakistan, one of the epicenters of COVID-19 in Asia. The estimated value of the important threshold parameter of the model, known as the basic reproduction number, is evaluated theoretically and numerically. Based on the real fitted parameters, we obtained R 0 ≈ 1.50 . Finally, an efficient numerical scheme of Adams-Moulton type is used in order to simulate the fractional model. The impact of some of the key model parameters on the disease dynamics and its elimination are shown graphically for various values of noninteger order of the Caputo derivative. We conclude that the use of fractional epidemic model provides a better understanding and biologically more insights about the disease dynamics.

A stochastic numerical analysis based on hybrid NAR-RBFs networks nonlinear SITR model for novel COVID-19 dynamics.

BACKGROUND: Mathematical modeling of vector-borne diseases and forecasting of epidemics outbreak are global challenges and big point of concern worldwide. The outbreaks depend on different social and demographic factors based on human mobility structured with the help of mathematical models for vector-borne disease transmission. In Dec 2019, an infectious disease is known as "coronavirus" (officially declared as COVID-19 by WHO) emerged in Wuhan (Capital city of Hubei, China) and spread quickly to all over the china with over 50,000 cases including more than 1000 death within a short period of one month. Multimodal modeling of robust dynamics system is a complex, challenging and fast growing area of the research. OBJECTIVES: The main objective of this proposed hybrid computing technique are as follows: The innovative design of the NAR-RBFs neural network paradigm is designed to construct the SITR epidemic differential equation (DE) model to ascertain the different features of the spread of COVID-19. The new set of transformations is introduced for nonlinear input to achieve with a higher level of accuracy, stability, and convergence analysis. METHODS: Multimodal modeling of robust dynamics system is a complex, challenging and fast growing area of the research. In this research bimodal spread of COVID-19 is investigated with hybrid model based on nonlinear autoregressive with radial base function (NAR-RBFs) neural network for SITR model. Chaotic and stochastic data of the pandemic. A new class of transformation is presented for the system of ordinary differential equation (ODE) for fast convergence and improvement of desired accuracy level. The proposed transformations convert local optimum values to global values before implementation of bimodal paradigm. RESULTS: This suggested NAR-RBFs model is investigated for the bi-module nature of SITR model with additional feature of fragility in modeling of stochastic variation ability for different cases and scenarios with constraints variation. Best agreement of the proposed bimodal paradigm with outstanding numerical solver is confirmed based on statistical results calculated from MSE, RMSE and MAPE with accuracy level based on mean square error up to 1E-25, which further validates the stability and consistence of bimodal proposed model. CONCLUSIONS: This computational technique is shown extraordinary results in terms of accuracy and convergence. The outcomes of this study will be useful in forecasting the progression of COVID-19, the influence of several deciding parameters overspread of COVID-19 and can help for planning, monitoring as well as preventing the spread of COVID-19.

On a new conceptual mathematical model dealing the current novel coronavirus-19 infectious disease.

The present paper describes a three compartment mathematical model to study the transmission of the current infection due to the novel coronavirus (2019-nCoV or COVID-19). We investigate the aforesaid dynamical model by using Atangana, Baleanu and Caputo (ABC) derivative with arbitrary order. We derive some existence results together with stability of Hyers-Ulam type. Further for numerical simulations, we use Adams-Bashforth (AB) method with fractional differentiation. The mentioned method is a powerful tool to investigate nonlinear problems for their respective simulation. Some discussion and future remarks are also given.

Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data.

We discuss a fractional-order SIRD mathematical model of the COVID-19 disease in the sense of Caputo in this article. We compute the basic reproduction number through the next-generation matrix. We derive the stability results based on the basic reproduction number. We prove the results of the solution existence and uniqueness via fixed point theory. We utilize the fractional Adams-Bashforth method for obtaining the approximate solution of the proposed model. We illustrate the obtained numerical results in plots to show the COVID-19 transmission dynamics. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.

Mathematical analysis of COVID-19 via new mathematical model.

We develop a new mathematical model by including the resistive class together with quarantine class and use it to investigate the transmission dynamics of the novel corona virus disease (COVID-19). Our developed model consists of four compartments, namely the susceptible class, S ( t ) , the healthy (resistive) class, H ( t ) , the infected class, I ( t ) and the quarantine class, Q ( t ) . We derive basic properties like, boundedness and positivity, of our proposed model in a biologically feasible region. To discuss the local as well as the global behaviour of the possible equilibria of the model, we compute the threshold quantity. The linearization and Lyapunov function theory are used to derive conditions for the stability analysis of the possible equilibrium states. We present numerical simulations to support our investigations. The simulations are compared with the available real data for Wuhan city in China, where the infection was initially originated.

Exploring Undergraduate Students’ Attitudes towards Emergency Online Learning during COVID-19: A Case from the UAE

This qualitative study aims to investigate the attitudes of undergraduate students towards their experience with emergency online learning during the first few weeks of the mandatory shift to online learning caused by COVID-19. Students from two general English courses at a university located in Abu Dhabi in United Arab Emirates were asked to write semi-guided essays during the week preceding the final exams of the second semester of the academic year 2019-20. A sample of these essays was analyzed using open coding. Findings revealed that cost- and time-effectiveness, safety, convenience and improved participation were the most frequently cited positive aspects of the emergency online learning experience, while distraction and reduced focus, heavy workload, problems with technology and the internet, and insufficient support from instructors and colleagues were the most recurrent negative aspects. The findings of the study help instructors and institutions understand students’ attitudes regarding online learning under abnormal circumstances. A number of recommendations informed by the interpretation of the participants’ feedback are offered to assist instructors, administrators and policy makers improve future online learning experiences.

On modeling of coronavirus-19 disease under Mittag-Leffler power law.

This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as ( ABC ) . Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered model and its uniqueness. Also, some results about stability of Ulam-Hyers type are also established. By applying a numerical technique called fractional Adams-Bashforth (AB) method, we develop a scheme for the approximate solutions to the considered model. Using some real available data, we perform the concerned numerical simulation corresponding to different values of fractional order.

Non Pharmaceutical Interventions for Optimal Control of COVID-19.

BACKGROUND AND OBJECTIVE: The outbreak of the current pandemic begun from the first individual of a 55-year old from Hubei province in China, the disease instigated by the new coronavirus spreading across the world. Scientists presently speculate this coronavirus, SARS-CoV-2, originated in a bat and by one way or another jumped to another creature, potentially the pangolin, which at that point gave it to people. The ailment is currently spreading between individuals with no animal delegate. Researchers are struggling to follow the infection back to where it started to become familiar with its spread. In the event that, for example, specialists can locate the soonest cases, they might have the option to distinguish the creature have where the infection hides. In March and April 2020, researchers detailed that this virus created normally. Coronavirus has been become of the serious global phenomena in the recent years and has negative effects in the entire world health and economy. The virus is believed to have been associated with a host animal which human contracted. Subsequently, human-to-human infection began. Through migration as humans have become complex with easy mobility the disease has traveled to the entire continent. Now, numerous scientist are going on in the hope of obtaining medication and vaccination to prevent the spread of the disease and mortality of the disease. It is important that we obtain quantitative and qualitative information about the etiology of this disease which is crucial. Mathematical modeling is capable of providing qualitative information on many parameters that guides the decision making of health practitioners. In this work we focus the optimal control of COVID-19 with the help of Non Pharmaceutical Interventions (NPIs). To find the role of factors/parameters in the transmission of the syndrome we find R0; the ratio of reproduction for the proposed model. METHODS: To find the role of parameters in the transmission of the syndrome we find R0; the ratio of reproduction for the proposed model. On the basis of sensitivity indices of the parameters we apply Non Pharmaceutical Interventions(NPIs) to control the sensitive parameters and hence formulate the optimal control mode. With the help of Hamiltonian and Lagrangian we minimize the density of contaminated stuff and infected human population. RESULTS: We focus the optimal control of COVID-19 with the help of Non Pharmaceutical Interventions(NPIs). On the basis of sensitivity indices of the parameters we apply Non Pharmaceutical Interventions(NPIs) to control the sensitive parameters and hence formulate the optimal control model. The major NPIs are, STAY HOME, SANITIZER (wash hands), EARLY CASE DETECTION (PCR Test) and FACE MASK. These NPIs helps in mitigation and reducing the size of outbreak of the disease. CONCLUSION: We check the existence of the optimal solution for the system. At the end, Using matlab we produce numerical simulations for validation of results of control variables. The results demonstrate that if there is no control (variables/interventios), 900 out 1000 susceptible individuals may be infected (exposed) in very short period. As such a circumstances no agency fighting against COVID-19 could be successful due to its limited resources.