Analysis and simulation study of the HIV/AIDS model using the real cases.

We construct a model to investigate HIV/AIDS dynamics in real cases and study its mathematical analysis. The study examines the qualitative outcomes and confirms the local and global asymptotic stability of both the endemic equilibrium and the disease-free equilibrium. The model's criteria for exhibiting both local and global asymptotically stable behavior are examined. We compute the endemic equilibria and obtain the existence of a unique positive endemic equilibrium. The data is fitted to the model using the idea of nonlinear least-squares fitting. Accurate parameter values are achieved by fitting the data to the model using a 95% confidence interval. The basic reproduction number is computed using parameters that have been fitted or estimated. Sensitivity analysis is performed to discover the influential parameters that impact the reproduction number and the eradication of the disease. The results show that implementing preventive measures can reduce HIV/AIDS cases.

Qualitative Analysis of the Transmission Dynamics of Dengue with the Effect of Memory, Reinfection, and Vaccination.

Dengue fever has a huge impact on people's physical, social, and economic lives in low-income locations worldwide. Researchers use epidemic models to better understand the transmission patterns of dengue fever in order to recommend effective preventative measures and give data for vaccine and treatment development. We use fractional calculus to organise the transmission phenomena of dengue fever, including immunisation, reinfection, therapy, and asymptotic carriers. In addition, we focused our study on the dynamical behavior and qualitative approach of dengue infection. The existence and uniqueness of the solution of the suggested dengue dynamics are inspected through the fixed point theorems of Schaefer and Banach. The Ulam-Hyers stability of the suggested dengue model is established. To illustrate the contribution of the input factors on the system of dengue infection, the solution paths are studied using the Laplace Adomian decomposition approach. Furthermore, numerical simulations are used to show the effects of fractional-order, immunity loss, vaccination, asymptotic fraction, biting rate, and therapy. We have established that asymptomatic carriers, bite rates, and immunity loss rates are all important factors that might make controlling more challenging. The intensity of dengue fever may be controlled by reducing mosquito bite rates, whereas the asymptotic fraction is risky and can transmit the illness to noninfected regions. Vaccination, fractional order, index of memory, and medication can be employed as proper control parameters.

LBCEPred: a machine learning model to predict linear B-cell epitopes.

B-cell epitopes have the capability to recognize and attach to the surface of antigen receptors to stimulate the immune system against pathogens. Identification of B-cell epitopes from antigens has a great significance in several biomedical and biotechnological applications, provides support in the development of therapeutics, design and development of an epitope-based vaccine and antibody production. However, the identification of epitopes with experimental mapping approaches is a challenging job and usually requires extensive laboratory efforts. However, considerable efforts have been placed for the identification of epitopes using computational methods in the recent past but deprived of considerable achievements. In this study, we present LBCEPred, a python-based web-tool (http://lbcepred.pythonanywhere.com/), build with random forest classifier and statistical moment-based descriptors to predict the B-cell epitopes from the protein sequences. LBECPred outperforms all sequence-based available models that are currently in use for the B-cell epitopes prediction, with 0.868 accuracy value and 0.934 area under the curve. Moreover, the prediction performance of proposed models compared to other state-of-the-art models is 56.3% higher on average for Mathews Correlation Coefficient. LBCEPred is easy to use tool even for novice users and has also shown the models stability and reliability, thus we believe in its significant contribution to the research community and the area of bioinformatics.

A comprehensive tool for accurate identification of methyl-Glutamine sites.

Methylation is a biochemical process involved in nearly all of the human body functions. Glutamine is considered an indispensable amino acid that is susceptible to methylation via post-translational modification (PTM). Modern research has proved that methylation plays a momentous role in the progression of most types of cancers. Therefore, there is a need for an effective method to predict glutamine sites vulnerable to methylation accurately and inexpensively. The motive of this study is the formulation of an accurate method that could predict such sites with high accuracy. Various computationally intelligent classifiers were employed for their formulation and evaluation. Rigorous validations prove that deep learning performs best as compared to other classifiers. The accuracy (ACC) and the area under the receiver operating curve (AUC) obtained by 10-fold cross-validation was 0.962 and 0.981, while with the jackknife testing, it was 0.968 and 0.980, respectively. From these results, it is concluded that the proposed methodology works sufficiently well for the prediction of methyl-glutamine sites. The webserver's code, developed for the prediction of methyl-glutamine sites, is freely available at https://github.com/s20181080001/WebServer.git. The code can easily be set up by any intermediate-level Python user.

Identification of stress response proteins through fusion of machine learning models and statistical paradigms.

Proteins are a vital component of cells that perform physiological functions to ensure smooth operations of bodily functions. Identification of a protein's function involves a detailed understanding of the structure of proteins. Stress proteins are essential mediators of several responses to cellular stress and are categorized based on their structural characteristics. These proteins are found to be conserved across many eukaryotic and prokaryotic linkages and demonstrate varied crucial functional activities inside a cell. The in-vivo, ex vivo, and in-vitro identification of stress proteins are a time-consuming and costly task. This study is aimed at the identification of stress protein sequences with the aid of mathematical modelling and machine learning methods to supplement the aforementioned wet lab methods. The model developed using Random Forest showed remarkable results with 91.1% accuracy while models based on neural network and support vector machine showed 87.7% and 47.0% accuracy, respectively. Based on evaluation results it was concluded that random-forest based classifier surpassed all other predictors and is suitable for use in practical applications for the identification of stress proteins. Live web server is available at http://biopred.org/stressprotiens , while the webserver code available is at https://github.com/abdullah5naveed/SRP_WebServer.git.

4mC-RF: Improving the prediction of 4mC sites using composition and position relative features and statistical moment.

N4-methylcytosine (4 mC) is an important epigenetic modification that occurs enzymatically by the action of DNA methyltransferases. 4 mC sites exist in prokaryotes and eukaryotes while playing a vital role in regulating gene expression, DNA replication, and cell cycle. The efficient and accurate prediction of 4 mC sites has a significant role in the insight of 4 mC biological properties and functions. Therefore, a sequence-based predictor is proposed, namely 4 mC-RF, for identifying 4 mC sites through the integration of statistical moments along with position, and composition-dependent features. Relative and absolute position-based features are computed to extract optimal features. A popular machine learning classifier Random Forest was used for training the model. Validation results were obtained through rigorous processes of self-consistency, 10-fold cross-validation, Independent set testing, and Jackknife yielding 95.1%, 95.2%, 97.0%, and 94.7% accuracies, respectively. Our proposed model depicts the highest prediction accuracies as compared to existing models. Subsequently, the developed 4 mC-RF model was constructed into a web server. A significant and more accurate predictor of 4 mC Methylcytosine sites helps experimental scientists to gather faster, efficient, and cost-effective results.

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.

Numerical approach towards gyrotactic microorganisms hybrid nanoliquid flow with the hall current and magnetic field over a spinning disk.

The article explores the effect of Hall current, thermal radiation, and magnetic field on hybrid nanofluid flow over the surface of a spinning disk. The motive of the present effort is to upgrade the heat transmission rate for engineering and industrial purposes. The hybrid nanofluids as compared to the conventional fluids have higher thermal properties. Therefore, in the present article, a special class of nanoparticles known as carbon nanotubes (CNTs) and iron ferrite nanoparticles are used in the base fluid. The system of modeled equations is depleted into dimensionless differential equations through similarity transformation. The transform equations are further solved through the Parametric Continuation method (PCM). For the parametric study, the physical parameters impact on velocity, energy, mass transmission, and motile microorganism's concentration profiles have been sketched. The obtained results are compared with the existing literature, which shows the best settlement. It concluded that the heat transmission rate reduces for Hall current and rises with radiative parameter. The results perceived that the addition of CNTs in carrier fluid is more efficacious than any other types of nanoparticles, due to its C-C bond. CNTs nanofluid can be more functionalized for the desired achievement, which can be utilized for a variety of applications by functionalization of non-covalent and covalent modification.

Crowding effects on the dynamics of COVID-19 mathematical model.

A disastrous coronavirus, which infects a normal person through droplets of infected person, has a route that is usually by mouth, eyes, nose or hands. These contact routes make it very dangerous as no one can get rid of it. The significant factor of increasing trend in COVID19 cases is the crowding factor, which we named "crowding effects". Modeling of this effect is highly necessary as it will help to predict the possible impact on the overall population. The nonlinear incidence rate is the best approach to modeling this effect. At the first step, the model is formulated by using a nonlinear incidence rate with inclusion of the crowding effect, then its positivity and proposed boundedness will be addressed leading to model dynamics using the reproductive number. Then to get the graphical results a nonstandard finite difference (NSFD) scheme and fourth order Runge-Kutta (RK4) method are applied.

Dynamics of COVID-19 mathematical model with stochastic perturbation.

Acknowledging many effects on humans, which are ignored in deterministic models for COVID-19, in this paper, we consider stochastic mathematical model for COVID-19. Firstly, the formulation of a stochastic susceptible-infected-recovered model is presented. Secondly, we devote with full strength our concentrated attention to sufficient conditions for extinction and persistence. Thirdly, we examine the threshold of the proposed stochastic COVID-19 model, when noise is small or large. Finally, we show the numerical simulations graphically using MATLAB.

A biological mathematical model of vector-host disease with saturated treatment function and optimal control strategies.

The aims of this paper to explore the dynamics of the vector-host disease with saturated treatment function. Initially, we formulate the model by considering three different classes for human and two for the vector population. The use of the treatment function in the model and their brief analysis for the case of disease-free and endemic case are briefly shown. We show that the basic reproduction number (< or >) than unity, the disease-free and endemic cases are stable locally and globally. Further, we apply the optimal control technique by choosing four control variables in order to maximize the population of susceptible and recovered human and to minimize the population of infected humans and vector. We discuss the results in details of the optimal controls model and show their existence. Furthermore, we solve the optimality system numerically in connection with the system of no control and the optimal control characterization together with adjoint system, and consider a set of different controls to simulate the models. The considerable best possible strategy that can best minimize the infection in human infected individuals is the use of all controls simultaneously. Finally, we conclude that the work with effective control strategies.

The dynamics of COVID-19 with quarantined and isolation.

In the present paper, we formulate a new mathematical model for the dynamics of COVID-19 with quarantine and isolation. Initially, we provide a brief discussion on the model formulation and provide relevant mathematical results. Then, we consider the fractal-fractional derivative in Atangana-Baleanu sense, and we also generalize the model. The generalized model is used to obtain its stability results. We show that the model is locally asymptotically stable if R 0 < 1 . Further, we consider the real cases reported in China since January 11 till April 9, 2020. The reported cases have been used for obtaining the real parameters and the basic reproduction number for the given period, R 0 ≈ 6.6361 . The data of reported cases versus model for classical and fractal-factional order are presented. We show that the fractal-fractional order model provides the best fitting to the reported cases. The fractional mathematical model is solved by a novel numerical technique based on Newton approach, which is useful and reliable. A brief discussion on the graphical results using the novel numerical procedures are shown. Some key parameters that show significance in the disease elimination from the society are explored.

Mathematical Model for Coronavirus Disease 2019 (COVID-19) Containing Isolation Class.

The deadly coronavirus continues to spread across the globe, and mathematical models can be used to show suspected, recovered, and deceased coronavirus patients, as well as how many people have been tested. Researchers still do not know definitively whether surviving a COVID-19 infection means you gain long-lasting immunity and, if so, for how long? In order to understand, we think that this study may lead to better guessing the spread of this pandemic in future. We develop a mathematical model to present the dynamical behavior of COVID-19 infection by incorporating isolation class. First, the formulation of model is proposed; then, positivity of the model is discussed. The local stability and global stability of proposed model are presented, which depended on the basic reproductive. For the numerical solution of the proposed model, the nonstandard finite difference (NSFD) scheme and Runge-Kutta fourth order method are used. Finally, some graphical results are presented. Our findings show that human to human contact is the potential cause of outbreaks of COVID-19. Therefore, isolation of the infected human overall can reduce the risk of future COVID-19 spread.

Entropy Generation of Carbon Nanotubes Flow in a Rotating Channel with Hall and Ion-Slip Effect Using Effective Thermal Conductivity Model.

This article examines the entropy analysis of magnetohydrodynamic (MHD) nanofluid flow of single and multiwall carbon nanotubes between two rotating parallel plates. The nanofluid flow is taken under the existence of Hall current and ion-slip effect. Carbon nanotubes (CNTs) are highly proficient heat transmission agents with bordering entropy generation and, thus, are considered to be a capable cooling medium. Entropy generation and Hall effect are mainly focused upon in this work. Using the appropriate similarity transformation, the central partial differential equations are changed to a system of ordinary differential equations, and an optimal approach is used for solution purposes. The resultant non-dimensional physical parameter appear in the velocity and temperature fields discussed using graphs. Also, the effect of skin fraction coefficient and Nusselt number of enclosed physical parameters are discussed using tables. It is observed that increased values of magnetic and ion-slip parameters reduce the velocity of the nanofluids and increase entropy generation. The results reveal that considering higher magnetic forces results in greater conduction mechanism.

Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model.

This paper studies the global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with appropriate initial and mixed boundary conditions. Under some practicable regularity criteria on diffusion item and nonlinearity, we establish the local existence and uniqueness of classical solutions based on a contraction mapping. This local solution can be continued for all positive time by employing the methods of energy estimates, Lp-theory, and Schauder estimate of linear parabolic equations. A straightforward application of global existence result of classical solutions to a density-dependent diffusion model of in vitro glioblastoma growth is also presented.

New operational matrices for solving fractional differential equations on the half-line.

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

Reversing invasion in bistable systems.

In this paper, we discuss a class of bistable reaction-diffusion systems used to model the competitive interaction of two species. The interactions are assumed to be of classic "Lotka-Volterra" type and we will consider a particular problem with relevance to applications in population dynamics: essentially, we study under what conditions the interplay of relative motility (diffusion) and competitive strength can cause waves of invasion to be halted and reversed. By establishing rigorous results concerning related degenerate and near-degenerate systems, we build a picture of the dependence of the wave speed on system parameters. Our results lead us to conjecture that this class of competition model has three "zones of response". In the central zone, varying the motility can slow, halt and reverse invasion. However, in the two outer zones, the direction of invasion is independent of the relative motility and is entirely determined by the relative competitive strengths. Furthermore, we conjecture that for a large class of competition models of the type studied here, the wave speed is an increasing function of the relative motility.