Heat transfer analysis: convective-radiative moving exponential porous fins with internal heat generation.

The efficiency, temperature distribution, and temperature at the tip of straight rectangular, growing and decaying moving exponential fins are investigated in this article. The influence of internal heat generation, surface and surrounding temperatures, convection-conduction, Peclet number and radiation-conduction is studied numerically on the efficiency, temperature profile, and temperature at the tip of the fin. Differential transform method is used to investigate the problem. It is revealed that thermal and thermo-geometric characteristics have a significant impact on the performance, temperature distribution, and temperature of the fin's tip.The results show that the temperature distribution of decaying exponential and rectangular fins is approximately 15 and 7% higher than growing exponential and rectangular fins respectively. It is estimated that the temperature distribution of the fin increases by approximately 6% when the porosity parameter is increased from 0.1 to 0.5. It is also observed that the decay exponential fin has better efficiency compared to growing exponential fin which offers significant advantages in mechanical engineering.

Correlated stochastic epidemic model for the dynamics of SARS-CoV-2 with vaccination.

In this paper, we propose a mathematical model to describe the influence of the SARS-CoV-2 virus with correlated sources of randomness and with vaccination. The total human population is divided into three groups susceptible, infected, and recovered. Each population group of the model is assumed to be subject to various types of randomness. We develop the correlated stochastic model by considering correlated Brownian motions for the population groups. As the environmental reservoir plays a weighty role in the transmission of the SARS-CoV-2 virus, our model encompasses a fourth stochastic differential equation representing the reservoir. Moreover, the vaccination of susceptible is also considered. Once the correlated stochastic model, the existence and uniqueness of a positive solution are discussed to show the problem's feasibility. The SARS-CoV-2 extinction, as well as persistency, are also examined, and sufficient conditions resulted from our investigation. The theoretical results are supported through numerical/graphical findings.

Entropy generation from convective-radiative moving exponential porous fins with variable thermal conductivity and internal heat generations.

The performance and thermal properties of convective-radiative rectangular and moving exponential porous fins with variable thermal conductivity together with internal heat generation are investigated. The second law of thermodynamics is used to investigate entropy generation in the proposed fins. The model is numerically solved using shooting technique. It is observed that the entropy generation depends on porosity parameter, temperature ratio, temperature distribution, thermal conductivity and fins structure. It is noted that entropy generation for a decay exponential fin is higher than that of a rectangular fin which is greater than that of a growing exponential fin. Moreover, entropy generation decreases as thermal conductivity increases. The results also reveal that entropy generation is maximum at the fin's base and the average entropy production depends on porosity parameters and temperature ratio. It is further reveal that the temperature ratio has a smaller amount of influence on entropy as compared to porosity parameter. It is concluded that when the temperature ratio is increases from 1.1 to 1.9, the entropy generation number is also increase by [Formula: see text] approximately. However, increasing porosity from 1 to 80 gives 14-fold increase in average entropy generation.

Mathematical modeling and thermodynamics of Prandtl-Eyring fluid with radiation effect: a numerical approach.

Main concern of current research is to develop a novel mathematical model for stagnation-point flow of magnetohydrodynamic (MHD) Prandtl-Eyring fluid over a stretchable cylinder. The thermal radiation and convective boundary condition are also incorporated. The modeled partial differential equations (PDEs) with associative boundary conditions are deduced into coupled non-linear ordinary differential equations (ODEs) by utilizing proper similarity transformations. The deduced dimensionless set of ODEs are solved numerically via shooting method. Behavior of controlling parameters on the fluid velocity, temperature fields as well as skin friction and Nusselt number are highlighted through graphs. Outcome declared that dimensionless fluid temperature boosts up for both the radiation parameter and Biot number. It is also revealed that the magnitude of both heat transfer rate and skin friction enhance for higher estimation of curvature parameter. Furthermore, comparative analysis between present and previous reports are provided for some specific cases to verify the obtained results.

A mathematical model for the dynamics of SARS-CoV-2 virus using the Caputo-Fabrizio operator.

The pandemic of SARS-CoV-2 virus remains a pressing issue with unpredictable characteristics which spread worldwide through human interactions. The current study is focusing on the investigation and analysis of a fractional-order epidemic model that discusses the temporal dynamics of the SARS-CoV-2 virus in a community. It is well known that symptomatic and asymptomatic individuals have a major effect on the dynamics of the SARS-CoV-2 virus therefore, we divide the total population into susceptible, asymptomatic, symptomatic, and recovered groups of the population. Further, we assume that the vaccine confers permanent immunity because multiple vaccinations have commenced across the globe. The new fractional-order model for the transmission dynamics of SARS-CoV-2 virus is formulated via the Caputo-Fabrizio fractional-order approach with the maintenance of dimension during the process of fractionalization. The theory of fixed point will be used to show that the proposed model possesses a unique solution whereas the well-posedness (bounded-ness and positivity) of the fractional-order model solutions are discussed. The steady states of the model are analyzed and the sensitivity analysis of the basic reproductive number is explored. Moreover to parameterize the model a real data of SARS-CoV-2 virus reported in the Sultanate of Oman from January 1st, 2021 to May 23rd, 2021 are used. We then perform the large scale numerical findings to show the validity of the analytical work.

Modeling the dynamics of novel coronavirus (COVID-19) via stochastic epidemic model.

In this article we propose a stochastic model to discuss the dynamics of novel corona virus disease. We formulate the model to study the long run behavior in varying population environment. For this purposes we divided the total human population into three epidemiological compartments: the susceptible, covid-19 infected, recovered and recovered along with one class of reservoir. The existence and uniqueness of the newly formulated model will be studied to show the well-possedness of the model. Moreover, we investigate the extinction analysis as well as the persistence analysis to find the disease extinction and disease persistence conditions. At the end we perform simulation to justify the investigation of analytical work with the help of graphical representations.

Modeling the transmission dynamics of middle eastern respiratory syndrome coronavirus with the impact of media coverage.

Middle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. In this paper, we propose a deterministic mathematical model to investigate the effect of media coverage on the transmission and control of Middle Eastern respiratory syndrome coronavirus disease. In order to do this we develop model formulation. Basic reproduction number R 0 will be calculated from the model to assess the transmissibility of the (MERS-CoV). We discuss the existence of backward bifurcation for some range of parameters. We also show stability of the model to figure out the stability condition and impact of media coverage. We show a special case of the model for which the endemic equilibrium is globally asymptotically stable. Finally all the theoretical results will be verified with the help of numerical simulation for easy understanding.

Modeling the pandemic trend of 2019 Coronavirus with optimal control analysis.

In this work, we propose a mathematical model to analyze the outbreak of the Coronavirus disease (COVID-19). The proposed model portrays the multiple transmission pathways in the infection dynamics and stresses the role of the environmental reservoir in the transmission of the disease. The basic reproduction number R 0 is calculated from the model to assess the transmissibility of the COVID-19. We discuss sensitivity analysis to clarify the importance of epidemic parameters. The stability theory is used to discuss the local as well as the global properties of the proposed model. The problem is formulated as an optimal control one to minimize the number of infected people and keep the intervention cost as low as possible. Medical mask, isolation, treatment, detergent spray will be involved in the model as time dependent control variables. Finally, we present and discuss results by using numerical simulations.

Existence, uniqueness, and stability of fractional hepatitis B epidemic model.

This paper describes the existence and stability of the hepatitis B epidemic model with a fractional-order derivative in Atangana-Baleanu sense. Some new results are handled by using the Sumudu transform. The existence and uniqueness of the equilibrium solution are presented using the Banach fixed-point theorem. Moreover, sensitivity analysis complemented by simulations is performed to determine how changes in parameters affect the dynamical behavior of the system. The numerical simulations are carried out using a predictor-corrector scheme to demonstrate the obtained results.

A stochastic SACR epidemic model for HBV transmission.

In this article, a stochastic SACR hepatitis B epidemic model is taken to be under consideration. We develop a stochastic epidemic model by considering the effect of environmental fluctuation on the hepatitis B dynamics and distribute the transmission rate by white noise. Using the stochastic Lyapunov function theory, we have shown the existence and uniqueness of the global positive solution. The extinction and persistence for our proposed model are derived with sufficient conditions. The numerical simulations are carried out using first-order Itô-Taylor stochastic scheme in the last section for the verification of our theoretical results.

Mathematical analysis of spread and control of the novel corona virus (COVID-19) in China.

Number of well-known contagious diseases exist around the world that mainly include HIV, Hepatitis B, influenzas etc., among these, a recently contested coronavirus (COVID-19) is a serious class of such transmissible syndromes. Abundant scientific evidence the wild animals are believed to be the primary hosts of the virus. Majority of such cases are considered to be human-to-human transmission, while a few are due to wild animals-to-human transmission and substantial burdens on healthcare system following this spread. To understand the dynamical behavior such diseases, we fitted a susceptible-infectious-quarantined model for human cases with constant proportions. We proposed a model that provide better constraints on understanding the climaxes of such unseen disastrous spread, relevant consequences, and suggesting future imperative strategies need to be adopted. The main features of the work include the positivity, boundedness, existence and uniqueness of solution of the model. The conditions were derived under which the COVID-19 may extinct or persist in the population. Sensitivity and estimation of those important parameters have been carried out that plays key role in the transmission mechanism. To optimize the spread of such disease, we present a control problem for further analysis using two control measures. The necessary conditions have been derived using the Pontryagin's maximum principle. Parameter values have been estimated from the real data and experimental numerical simulations are presented for comparison as well as verification of theoretical results. The obtained numerical results also present the verification, accuracy, validation, and robustness of the proposed scheme.

Co-infection of Middle Eastern respiratory syndrome coronavirus and pulmonary tuberculosis.

Co-infection of Middle Eastern respiratory syndrome, coronavirus and tuberculosis, TB has a complex clinical entities that has estimated worldwide; mostly, in the Middle East. Clinical studies have shown that the propagation of disease is faster in (MERS-CoV) and TB co-infection compared to those of mono-infection. Clinical reports have shown that treatment of tuberculosis (TB) increase the risk of (MERS-CoV) reactivation. In this article, we propose an epidemic model to represents the Middle East respiratory syndrome coronavirus and tuberculosis (TB) co-infection. To do this, we first find the basic reproductive number and analyze the stability of the model. The stability conditions are obtained in term of the basic reproductive number. We also study the bifurcation analysis of the model, using the central manifold theory. Sensitivity of the basic reproductive number is performed to understand the most sensitive parameters. Finally, we show the feasibility of the analytical work, by numerical simulation.

Stability analysis of leishmania epidemic model with harmonic mean type incidence rate.

We discussed anthroponotic cutaneous leishmania transmission in this article, due to its large effect on the community in the recent years. The mathematical model is developed for anthroponotic cutaneous leishmania transmission, and its qualitative behavior is taken under consideration. The threshold number R 0 of the model is derived using the next-generation method. In the disease-free case, local and global stability is carried out with the condition that R 0 will be less than one. The global stability at the disease-free equilibrium point has been derived by utilizing the Castillo-Chavez method. On the other hand, at the endemic equilibrium point, the local and global stability holds with some conditions, and R 0 is greater than unity. The global stability at the endemic equilibrium point is established with the help of a geometrical approach which is the generalization of Lyapunov theory, by using the third additive compound matrix. The sensitivity analysis of the threshold number with other parameters is also taken into account. Several graphs of important parameters are discussed in the last section.

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.

Hopf bifurcation and global dynamics of time delayed Dengue model.

BACKGROUND AND OBJECTIVE: Dengue viral infections are a standout amongst the supreme critical mosquito-borne illnesses nowadays. They create problems like dengue fever (DF), dengue stun disorder (DSS) and dengue hemorrhagic fever (DHF). Lately, the frequency of DHF has expanded considerably. Dengue may be caused by one of serotypes DEN-1 to DEN-4. For the most part, septicity with one serotype presents upcoming defensive resistance against that specific serotype yet not against different serotypes. When anyone is infected for a second time with different serotypes, a serious ailment will occur. The proposed model focused on the dynamic interaction between susceptible cells and free virus cells. The ailment free steady states of the specimen are determined. The steadiness of the steady states has been examined by using Laplace transform. METHODS: We introduce an appropriate numerical technique based on an Adams Bash-forth Moulton method for non-integer order delay differential equations. The numerical simulations validate the accuracy and efficacy of the numerical method. RESULTS: In this paper, we study a non-integer order model with temporal delay to elaborate the dynamics of Dengue internal transmission dynamics. The temporal delay is presented in the susceptible cell and free virus cell. Centered on non-integer Laplace transform, some environs on firmness and Hopf bifurcation are derived for the model. Beside these global stability analysis is also done. Lastly, the imitative theoretical results are justified by few numerical simulations. CONCLUSION: The study spectacles that the non-integer order with temporal-delay can successfully enhance the dynamics and rejuvenate the steadiness terms of non-integer order septicity prototypes. Both the ailment free equilibrium (AFE) node and ailment persistent equilibrium (APE) node are steady for the given system. We deduce a recipe that regulates the critical value at threshold.

HIV-1 infection dynamics and optimal control with Crowley-Martin function response.

BACKGROUND AND OBJECTIVE: As we all know, mathematical models provide very important information for the study of the human immunodeficiency virus type. Mathematical model of human immunodeficiency virus type-1 (HIV-1) infection with contact rate represented by Crowley-Martin function response is taken into account. The aims of this novel study is to checkthe local and global stability of the disease and also prevent the outbreak from the community. METHODS: The mathematical model as well as optimal system of nonlinear differential equations are tackled numerically by Runge-Kutta fourth-order method. For global stability we use Lyapunov-LaSalle invariance principle and for the description of optimal control, Pontryagin's maximum principle is used. RESULTS: Graphical results are depicted and examined with different parameters values versus the basic reproductive number R0 and also the plots with and without control. The density of infected cells continued to increase without treatment, but the concentration of these cells decreased after treatment. The intensity of the pathogenic virus before and after the optimal treatment. This indicates a sharp drop in the rate of pathogenic viruses after treatment. It prevents the production of viruses by preventing cell infection and minimizing side effects. CONCLUSIONS: We analysed the model by defining the basic reproductive number, showing the boundedness, positivity and permanence of the solution, and proving the local and global stability of the infection-free state. We show that the threshold quantity R0 < 1, the elimination of HIV-1 infection from the T cell population, is eradicated; while for the threshold quantity R0 > 1, HIV-1 infection remains in the host. When the threshold quantity R0 > 1, then it shows that the steady-state of chronic disease is globally stable. Optimal control strategies are developed with the optimal control pair for the description of optimal control. To reduce the density of infected cells and viruses as well as maximize the density of healthy cells is determined by the objective functional.

Modeling and qualitative analysis of a hepatitis B epidemic model.

We develop an epidemic mathematical model for hepatitis B contagious disease, which is one of the major causes of death among various infectious diseases. We prove the existence, positivity, and biological feasibility of the model. We find the threshold quantity of the model and analyze the sensitivity analysis to show the effect of various parameters on the spread of hepatitis B virus. Exploiting the linear stability approach, we find stability conditions to perform the stability analysis. We use the central manifold theory to discuss the existence of backward bifurcation of the proposed model. Finally, we present numerical simulations to verify the analytical calculations and to analyze the sensitivity of parameters.

A stochastic model for the transmission dynamics of hepatitis B virus.

In this paper, we formulate a stochastic model for hepatitis B virus transmission with the effect of fluctuation environment. We divide the total population into four different compartments, namely, the susceptible individuals in which the disease transmission rate is distributed by white noise, the acutely infected individuals in which the same perturbation occur, the chronically infected individuals and the recovered individuals. We use the stochastic Lyapunov function theory to construct a suitable stochastic Lyapunov function for the existence of positive solution. We also then establish the sufficient conditions for the hepatitis B extinction and the hepatitis B persistence. At the end numerical simulation is carried out by using the stochastic Runge-Kutta method to support our analytical findings.

Existence theory and numerical solutions to smoking model under Caputo-Fabrizio fractional derivative.

In this paper, taking fractional derivative due to Caputo and Fabrizo, we have investigated a biological model of smoking type. By using Sumudu transform and Picard successive iterative technique, we develop the iterative solutions for the considered model. Furthermore, some results related to uniqueness of the equilibrium solution and its stability are discussed utilizing the techniques of nonlinear functional analysis. The dynamics of iterative solutions for various compartments of the model are plotted with the help of Matlab.

Magnetohydrodynamic fluid flow and heat transfer over a shrinking sheet under the influence of thermal slip.

We study the heat transfer of a Magneto Hydrodynamic (MHD) boundary layer flow of a Newtonian fluid over a pervious shrinking sheet under the influence of thermal slip. The flow allows electric current to pass through. The governing PDEs are transformed into self-similar ODEs via Lie group analysis. We study the variations in the dimensionless quantities like velocity and temperature of the flow in terms of the different parameters involved in the problem. We discuss the thickness of the boundary layers under the influence of various parameters involved in the flow. Numerical simulations are carried out to explain and support the results obtained.