Predictive dynamical modeling and stability of the equilibria in a discrete fractional difference COVID-19 epidemic model

The SARSCoV-2 virus, also known as the coronavirus-2, is the consequence of COVID-19, a severe acute respiratory syndrome. Droplets from an infectious individual are how the pathogen is transmitted from one individual to another and occasionally, these particles can contain toxic textures that could also serve as an entry point for the pathogen. We formed a discrete fractional-order COVID-19 framework for this investigation using information and inferences from Thailand. To combat the illnesses, the region has implemented mandatory vaccination, interpersonal stratification and mask distribution programs. As a result, we divided the vulnerable people into two groups: those who support the initiatives and those who do not take the influence regulations seriously. We analyze endemic problems and common data while demonstrating the threshold evolution defined by the fundamental reproductive quantity

Numerical treatments for the optimal control of two types variable-order COVID-19 model.

In this paper, a novel variable-order COVID-19 model with modified parameters is presented. The variable-order fractional derivatives are defined in the Caputo sense. Two types of variable order Caputo definitions are presented here. The basic reproduction number of the model is derived. Properties of the proposed model are studied analytically and numerically. The suggested optimal control model is studied using two numerical methods. These methods are non-standard generalized fourth-order Runge-Kutta method and the non-standard generalized fifth-order Runge-Kutta technique. Furthermore, the stability of the proposed methods are studied. To demonstrate the methodologies' simplicity and effectiveness, numerical test examples and comparisons with real data for Egypt and Italy are shown.

Bio-Inspired Modelling of Disease Through Delayed Strategies

In 2020, the reported cases were 0.12 million in the six regions to the official report of the World Health Organization (WHO). For most children infected with leprosy, 0.008629 million cases were detected under fifteen. The total infected ratio of the children population is approximately 4.4 million. Due to the COVID-19 pandemic, the awareness programs implementation has been disturbed. Leprosy disease still has a threat and puts people in danger. Nonlinear delayed modeling is critical in various allied sciences, including computational biology, computational chemistry, computational physics, and computational economics, to name a few. The time delay effect in treating leprosy delayed epidemic model is investigated. The whole population is divided into four groups: those who are susceptible, those who have been exposed, those who have been infected, and those who have been vaccinated. The local and global stability of well-known conclusions like the Routh Hurwitz criterion and the Lyapunov function has been proven. The parameters’ sensitivity is also examined. The analytical analysis is supported by computer results that are presented in a variety of ways. The proposed approach in this paper preserves equilibrium points and their stabilities, the existence and uniqueness of solutions, and the computational ease of implementation.

Numerical Simulations on Scale-Free and Random Networks for the Spread of COVID-19 in Pakistan

Epidemiology is the study of how and why an infectious disease occurs in a group of people. Several epidemiological models have been developed to get information on the spread of a disease in society. That information is used to plan strategies to prevent illness and manage patients. But, most of these models consider only random diffusion of the disease and hence ignore the number of interactions among people. To take into account the interactions among individuals, the network approach is becoming increasingly popular. It is novel to consider the dynamics of infectious disease using various networks rather than classical differential equation models. In this paper, we numerically simulate the Susceptible-Infected-Recoverd (SIR) model on Barabási-Albert network and Erdös-Rényi network to analyze the spread of COVID-19 in Pakistan so that we know the severity of the disease. We also show how a situation becomes alarming if hubs in a network get infected.

APPLICATIONS OF GUDERMANNIAN NEURAL NETWORK FOR SOLVING THE SITR FRACTAL SYSTEM

This study is related to explore the Gudermannian neural network (GNN) for solving a nonlinear SITR COVID-19 fractal system by using the optimization efficiencies of a genetic algorithm (GA), a global search technique and sequential quadratic programming (SQP) and a quick local search scheme, i.e. GNN-GA-SQP. The nonlinear SITR COVID-19 fractal system is dependent on four collections: “susceptible”, “infected”, “treatment” and “recovered”. For the optimization procedures through the GNN-GA-SQP, a merit function is constructed using the nonlinear SITR COVID-19 fractal system and its corresponding initial conditions. The description of each collection of the nonlinear SITR COVID-19 fractal system is provided along with comprehensive detail. The comparison of the achieved numerical result performances of each collection of the nonlinear SITR COVID-19 fractal system is performed with the Adams results to verify the exactness of the designed computational GNN-GA-SQP. The statistical processes based on different operators are presented for 30 independent trials using 5 neurons to authenticate the consistency of the designed computational GNN-GA-SQP. Moreover, the graphs of absolute error (AE), performance indices, and convergence measures along with the boxplots and histograms are also plotted to check the stability, exactness and reliability of the designed computational GNN-GA-SQP. [ FROM AUTHOR] Copyright of Fractals is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full . (Copyright applies to all s.)

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.

Mathematical modeling and analysis of the novel Coronavirus using Atangana-Baleanu derivative.

The novel Coronavirus infection disease is becoming more complex for the humans society by giving death and infected cases throughout the world. Due to this infection, many countries of the world suffers from great economic loss. The researchers around the world are very active to make a plan and policy for its early eradication. The government officials have taken full action for the eradication of this virus using different possible control strategies. It is the first priority of the researchers to develop safe vaccine against this deadly disease to minimize the infection. Different approaches have been made in this regards for its elimination. In this study, we formulate a mathematical epidemic model to analyze the dynamical behavior and transmission patterns of this new pandemic. We consider the environmental viral concentration in the model to better study the disease incidence in a community. Initially, the model is constructed with the derivative of integer-order. The classical epidemic model is then reconstructed with the fractional order operator in the form of Atangana-Baleanu derivative with the nonsingular and nonlocal kernel in order to analyze the dynamics of Coronavirus infection in a better way. A well-known estimation approach is used to estimate model parameters from the COVID-19 cases reported in Saudi Arabia from March 1 till August 20, 2020. After the procedure of parameters estimation, we explore some basic mathematical analysis of the fractional model. The stability results are provided for the disease free case using fractional stability concepts. Further, the uniqueness and existence results will be shown using the Picard-Lendelof approach. Moreover, an efficient numerical scheme has been proposed to obtain the solution of the model numerically. Finally, using the real fitted parameters, we depict many simulation results in order to demonstrate the importance of various model parameters and the memory index on disease dynamics and possible eradication.

Caputo SIR model for COVID-19 under optimized fractional order.

Everyone is talking about coronavirus from the last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed, and as many as 180 countries have been so far affected with 928,287 (14 September 2020) deaths within a couple of months. Ironically, 29,185,779 are still active cases. Having seen such a drastic situation, a relatively simple epidemiological SIR model with Caputo derivative is suggested unlike more sophisticated models being proposed nowadays in the current literature. The major aim of the present research study is to look for possibilities and extents to which the SIR model fits the real data for the cases chosen from 1 April to 15 March 2020, Pakistan. To further analyze qualitative behavior of the Caputo SIR model, uniqueness conditions under the Banach contraction principle are discussed and stability analysis with basic reproduction number is investigated using Ulam-Hyers and its generalized version. The best parameters have been obtained via the nonlinear least-squares curve fitting technique. The infectious compartment of the Caputo SIR model fits the real data better than the classical version of the SIR model (Brauer et al. in Mathematical Models in Epidemiology 2019). Average absolute relative error under the Caputo operator is about 48% smaller than the one obtained in the classical case ( ν = 1 ). Time series and 3D contour plots offer social distancing to be the most effective measure to control the epidemic.

Factor analysis approach to classify COVID-19 datasets in several regions.

The aim of this research is to investigate the relationships between the counts of cases with Covid-19 and the deaths due to it in seven countries that are severely affected from this pandemic disease. First, the Pearson's correlation is used to determine the relationships among these countries. Then, the factor analysis is applied to categorize these countries based on their relationships.

Fractional unit-root tests allowing for a fractional frequency flexible Fourier form trend: predictability of Covid-19.

In this study we propose a fractional frequency flexible Fourier form fractionally integrated ADF unit-root test, which combines the fractional integration and nonlinear trend as a form of the Fourier function. We provide the asymptotics of the newly proposed test and investigate its small-sample properties. Moreover, we show the best estimators for both fractional frequency and fractional difference operator for our newly proposed test. Finally, an empirical study demonstrates that not considering the structural break and fractional integration simultaneously in the testing process may lead to misleading results about the stochastic behavior of the Covid-19 pandemic.

Analysis and Dynamics of Fractional Order Covid-19 Model with Memory Effect

The present article attempts to examine fractional order Covid-19 model by employing an efficient and powerful analytical scheme termed as q-homotopy analysis Sumudu transform method (q-HASTM). The q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. Liouville-Caputo approach of the fractional operator has been employed. The proposed modelis also examined numerically via generalized Adams-Bashforth-Moulton method. We determined model equilibria and also give their stability analysis by employing next generation matrix and fractional Routh-Hurwitz stability criterion.

Epidemiological Analysis of the Coronavirus Disease Outbreak with Random Effects

Today, coronavirus appears as a serious challenge to the whole world. Epidemiological data of coronavirus is collected through media and web sources for the purpose of analysis. New data on COVID-19 are available daily, yet information about the biological aspects of SARS-CoV-2 and epidemiological characteristics of COVID-19 remains limited, and uncertainty remains around nearly all its parameters’ values. This research provides the scientific and public health communities better resources, knowledge, and tools to improve their ability to control the infectious diseases. Using the publicly available data on the ongoing pandemic, the present study investigates the incubation period and other time intervals that govern the epidemiological dynamics of the COVID-19 infections. Formulation of the testing hypotheses for different countries with a 95% level of confidence, and descriptive statistics have been calculated to analyze in which region will COVID-19 fall according to the tested hypothesized mean of different countries. The results will be helpful in decision making as well as in further mathematical analysis and control strategy. Statistical tools are used to investigate this pandemic, which will be useful for further research. The testing of the hypothesis is done for the differences in various effects including standard errors. Changes in states’ variables are observed over time. The rapid outbreak of coronavirus can be stopped by reducing its transmission. Susceptible should maintain safe distance and follow precautionary measures regarding COVID-19 transmission.

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.

Optimal Control Model for the Transmission of Novel COVID-19

As the corona virus (COVID-19) pandemic ravages socio-economic activities in addition to devastating infectious and fatal consequences, optimal control strategy is an effective measure that neutralizes the scourge to its lowest ebb. In this paper, we present a mathematical model for the dynamics of COVID-19, and then we added an optimal control function to the model in order to effectively control the outbreak. We incorporate three main control efforts (isolation, quarantine and hospitalization) into the model aimed at controlling the spread of the pandemic. These efforts are further subdivided into five functions;u1(t) (isolation of the susceptible communities), u2(t) (contact track measure by which susceptible individuals with contact history are quarantined), u3(t) (contact track measure by which infected individualsare quarantined), u4(t) (control effort of hospitalizing the infected I1) and u5(t) (control effort of hospitalizing the infected I2). We establish the existence of the optimal control and also its characterization by applying Pontryaging maximum principle. The disease free equilibrium solution (DFE) is found to be locally asymptotically stable and subsequently we used it to obtain the key parameter;basic reproduction number. We constructed Lyapunov function to which global stability of the solutions is established. Numerical simulations show how adopting the available control measures optimally, will drastically reduce the infectious populations.

New applications related to Covid-19.

Analysis of mathematical models projected for COVID-19 presents in many valuable outputs. We analyze a model of differential equation related to Covid-19 in this paper. We use fractal-fractional derivatives in the proposed model. We analyze the equilibria of the model. We discuss the stability analysis in details. We apply very effective method to obtain the numerical results. We demonstrate our results by the numerical simulations.

Dynamics of COVID-19 via singular and non-singular fractional operators under real statistical observations

Coronavirus has paralyzed various socio-economic sectors worldwide. Such unprecedented outbreak was proved to be lethal for about 1,069,513 individuals based upon information released by Worldometers on October 09, 2020. In order to fathom transmission dynamics of the virus, different kinds of mathematical models have recently been proposed in literature. In the continuation, we have formulated a deterministic COVID-19 model under fractional operators using six nonlinear ordinary differential equations. Using fixed-point theory and Arzelá Ascoli principle, the proposed model is shown to have existence of unique solution while stability analysis for differential equations involved in the model is carried out via Ulam?Hyers and generalized Ulam?Hyers conditions in a Banach space. Real COVID-19 cases considered from July 01 to August 14, 2020, in Pakistan were used to validate the model, thereby producing best fitted values for the parameters via nonlinear least-squares approach while minimizing sum of squared residuals. Elasticity indices for each parameter are computed. Two numerical schemes under singular and non-singular operators are formulated for the proposed model to obtain various simulations of particularly asymptomatically infectious individuals and of control reproduction number Rc. It has been shown that the fractional operators with order α=9.8254e?01 generated Rc=2.5087 which is smaller than the one obtained under the classical case ( α=1). Interesting behavior of the virus is explained under fractional case for the epidemiologically relevant parameters. All results are illustrated from biological viewpoint.

A Mathematical and Statistical Estimation of Potential Transmission and Severity of COVID-19: A Combined Study of Romania and Pakistan.

During the outbreak of an epidemic, it is of immense interest to monitor the effects of containment measures and forecast of outbreak including epidemic peak. To confront the epidemic, a simple SIR model is used to simulate the number of affected patients of coronavirus disease in Romania and Pakistan. The model captures the growth in case onsets, and the estimated results are almost compatible with the actual reported cases. Through the calibration of parameters, forecast for the appearance of new cases in Romania and Pakistan is reported till the end of this year by analysing the current situation. The constant level of number of patients and time to reach this level is also reported through the simulations. The drastic condition is also discussed which may occur if all the preventive restraints are removed.

Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19 in Nigeria Using Atangana-Baleanu Operator

We propose a mathematical model of the coronavirus disease 2019 (COVID-19) to investigate the transmission and control mechanism of the disease in the community of Nigeria. Using stability theory of differential equations, the qualitative behavior of model is studied. The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix. Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease. Further, we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established. We consider the data of reported infection cases from April 1, 2020, till April 30, 2020, and parameterized the model. We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations. The impacts of various biological parameters on transmission dynamics of COVID-19 is examined. These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease. In the end, the obtained results are demonstrated graphically to justify our theoretical findings.