A mathematical model for the co-dynamics of COVID-19 and tuberculosis.

In this study, we formulated and analyzed a deterministic mathematical model for the co-infection of COVID-19 and tuberculosis, to study the co-dynamics and impact of each disease in a given population. Using each disease's corresponding reproduction number, the existence and stability of the disease-free equilibrium were established. When the respective threshold quantities R C , and R T are below unity, the COVID-19 and TB-free equilibrium are said to be locally asymptotically stable. The impact of vaccine (i.e., efficacy and vaccinated proportion) and the condition required for COVID-19 eradication was examined. Furthermore, the presence of the endemic equilibria of the sub-models is analyzed and the criteria for the phenomenon of backward bifurcation of the COVID-19 sub-model are presented. To better understand how each disease condition impacts the dynamics behavior of the other, we investigate the invasion criterion of each disease by computing the threshold quantity known as the invasion reproduction number. We perform a numerical simulation to investigate the impact of threshold quantities ( R C , R T ) with respect to their invasion reproduction number, co-infection transmission rate ( ß c t ) , and each disease transmission rate ( ß c , ß t ) on disease dynamics. The outcomes established the necessity for the coexistence or elimination of both diseases from the communities. Overall, our findings imply that while COVID-19 incidence decreases with co-infection prevalence, the burden of tuberculosis on the human population increases.

γ-Nanofluid Thermal Transport between Parallel Plates Suspended by Micro-Cantilever Sensor by Incorporating the Effective Prandtl Model: Applications to Biological and Medical Sciences.

The flow of nanofluid between infinite parallel plates suspended by micro-cantilever sensors is significant. The analysis of such flows is a rich research area due to the variety of applications it has in chemical, biological and medical sciences. Micro-cantilever sensors play a significant role in accurately sensing different diseases, and they can be used to detect many hazardous and bio-warfare agents. Therefore, flow water and ethylene glycol (EG) composed by γ-nanoparticles is used. Firstly, the governing nanofluid model is transformed into two self-similar nanofluid models on the basis of their effective models. Then, a numerical method is adopted for solution purposes, and both the nanofluid models are solved. To enhance the heat transfer characteristics of the models, the effective Prandtl model is ingrained in the energy equation. The velocity F'(η) decreases with respect to the suction of the fluid, because more fluid particles drags on the surface for suction, leading to an abrupt decrement in F'(η). The velocity F'(η) increases for injection of the fluid from the upper end, and therefore the momentum boundary layer region is prolonged. A high volume fraction factor is responsible for the denser characteristics of the nanofluids, due to which the fluids become more viscous, and the velocity F'(η) drops abruptly, with the magnetic parameters favoring velocity F'(η). An increase in temperature ß ( η ) of Al2O3-H2O and γAl2O3-C2H6O2 nanofluids was reported at higher fraction factors with permeable parameter effects. Finally, a comparative analysis is presented by restricting the flow parameters, which shows the reliability of the study.

Computational Study of the Coupled Mechanism of Thermophoretic Transportation and Mixed Convection Flow around the Surface of a Sphere.

The main goal of the current work was to study the coupled mechanism of thermophoretic transportation and mixed convection flow around the surface of the sphere. To analyze the characteristics of heat and fluid flow in the presence of thermophoretic transportation, a mathematical model in terms of non-linear coupled partial differential equations obeying the laws of conservation was formulated. Moreover, the mathematical model of the proposed phenomena was approximated by implementing the finite difference scheme and boundary value problem of fourth order code BVP4C built-in scheme. The novelty point of this paper is that the primitive variable formulation is introduced to transform the system of partial differential equations into a primitive form to make the line of the algorithm smooth. Secondly, the term thermophoretic transportation in the mass equation is introduced in the mass equation and thus the effect of thermophoretic transportation can be calculated at different positions of the sphere. Basically, in this study, some favorite positions around the sphere were located, where the velocity field, temperature distribution, mass concentration, skin friction, and rate of heat transfer can be calculated simultaneously without any separation in flow around the surface of the sphere.

Thermal Transport Investigation in Magneto-Radiative GO-MoS2/H2O-C2H6O2 Hybrid Nanofluid Subject to Cattaneo-Christov Model.

Currently, thermal investigation in hybrid colloidal liquids is noteworthy. It has applications in medical sciences, drug delivery, computer chips, electronics, the paint industry, mechanical engineering and to perceive the cancer cell in human body and many more. Therefore, the study is carried out for 3D magnetized hybrid nanofluid by plugging the novel Cattaneo-Christov model and thermal radiations. The dimensionless version of the model is successfully handled via an analytical technique. From the reported analysis, it is examined that Graphene Oxide-molybdenum disulfide/C2H6O2-H2O has better heat transport characteristics and is therefore reliable for industrial and technological purposes. The temperature of Graphene Oxide GO-molybdenum disulfide/C2H6O2-H2O enhances in the presence of thermal relaxation parameter and radiative effects. Also, it is noted that rotational velocity of the hybrid nanofluid rises for stronger magnetic parameter effects. Moreover, prevailed behavior of thermal conductivity of GO-molybdenum disulfide/C2H6O2-H2O is detected which shows that hybrid nanofluids are a better conductor as compared to that of a regular nanofluid.

Radiative Colloidal Investigation for Thermal Transport by Incorporating the Impacts of Nanomaterial and Molecular Diameters (dNanoparticles, dFluid): Applications in Multiple Engineering Systems.

Thermal enhancement and irreversible phenomena in colloidal suspension (Al2O3-H2O) is a potential topic of interest from the aspects of industrial, mechanical and thermal engineering; heat exchangers; coolant car radiators; and bio-medical, chemical and civil engineering. In the light of these applications, a colloidal analysis of Al2O3-H2O was made. Therefore, a colloidal model is considered and treated numerically. The significant influences of multiple parameters on thermal enhancement, entropy generation and Bejan parameter are examined. From the presented colloidal model, it is explored that Al2O3-H2O is better for the applications of mechanical and applied thermal engineering. Moreover, fraction factor tiny particles are significant parameters which enhanced the thermal capability of the Al2O3-H2O suspension.

Impacts of Freezing Temperature Based Thermal Conductivity on the Heat Transfer Gradient in Nanofluids: Applications for a Curved Riga Surface.

The flow of nanofluid over a curved Riga surface is a topic of interest in the field of fluid dynamics. A literature survey revealed that the impacts of freezing temperature and the diameter of nanoparticles on the heat transfer over a curved Riga surface have not been examined so far. Therefore, the flow of nanoparticles, which comprises the influences of freezing temperature and nanoparticle diameter in the energy equation, was modeled over a curved Riga surface. The model was reduced successfully in the nondimensional version by implementing the feasible similarity transformations and effective models of nanofluids. The coupled nonlinear model was then examined numerically and highlighted the impacts of various flow quantities in the flow regimes and heat transfer, with graphical aid. It was examined that nanofluid velocity dropped by increasing the flow parameters γ and S, and an abrupt decrement occurred at the surface of the Riga sheet. The boundary layer region enhances for larger γ. The temperature distribution was enhanced for a more magnetized nanofluid, and the thermal boundary layer increased with a larger R parameter. The volume fraction of the nanoparticles favors the effective density and dynamic viscosity of the nanofluids. A maximum amount of heat transfer at the surface was observed for a more magnetized nanofluid.

Mathematical model for spreading of COVID-19 virus with the Mittag-Leffler kernel.

In the Nidovirales order of the Coronaviridae family, where the coronavirus (crown-like spikes on the surface of the virus) causing severe infections like acute lung injury and acute respiratory distress syndrome. The contagion of this virus categorized as severed, which even causes severe damages to human life to harmless such as a common cold. In this manuscript, we discussed the SARS-CoV-2 virus into a system of equations to examine the existence and uniqueness results with the Atangana-Baleanu derivative by using a fixed-point method. Later, we designed a system where we generate numerical results to predict the outcome of virus spreadings all over India.

Entropy Generation in MHD Conjugate Flow with Wall Shear Stress over an Infinite Plate: Exact Analysis.

The current work will describe the entropy generation in an unsteady magnetohydrodynamic (MHD) flow with a combined influence of mass and heat transfer through a porous medium. It will consider the flow in the XY plane and the plate with isothermal and ramped wall temperature. The wall shear stress is also considered. The influences of different pertinent parameters on velocity, the Bejan number and on the total entropy generation number are reported graphically. Entropy generation in the fluid is controlled and reduced on the boundary by using wall shear stress. It is observed in this paper that by taking suitable values of pertinent parameters, the energy losses in the system can be minimized. These parameters are the Schmitt number, mass diffusion parameter, Prandtl number, Grashof number, magnetic parameter and modified Grashof number. These results will play an important role in the heat flow of uncertainty and must, therefore, be controlled and managed effectively.

Modeling and analysis of Hepatitis B dynamics with vaccination and treatment with novel fractional derivative.

These days, fractional calculus is essential for studying the dynamic transmission of illnesses, developing control systems, and solving several other real-world issues. In this study, we develop a Hepatitis B (HBV) model to observe the dynamics of vaccination and treatment effects to control the disease by using novel fractional operator. Modified Atangana-Baleanu-Caputo (MABC) is a new definition of the used derivative that is based on a modification of the Atangana and Baleanu derivatives. By employing the MABC fractional derivative, which incorporates the concepts of non-locality and memory effects our model captures the complex dynamics of HBV transmission more accurately than traditional models. An objective of this study is to analyze the effect of immunization and treatment techniques on the course of the hepatitis B virus, with a particular focus on the changing order of differentiation. Thereby, our paper deals with the stability analysis, positiveness, existence and uniqueness of the solution and simulations. Analysis of reproductive number R0 with the impact of different parameters is also treated. The proposed model's existence and uniqueness findings are examined through the use of Banach's fixed point and Leray-Schauder nonlinear alternative theorems. The equilibria for the models are determined to be globally stable using Lyapunov functions. The simulations for certain parameters are achieved by applying the Lagrange interpolation for the numerical computations and also the results are compared with the ABC operator results. The model is validated using numerical simulations, which are also used to assess how well different intervention techniques work to lower the impact of HBV infection and prevent its spread throughout the community. The results of this research assist in developing public health policies intended to lower the incidence of HBV infection worldwide and offer insightful information about how well treatment and vaccination strategies work to prevent HBV disease.

Optimal and total controllability approach of non-instantaneous Hilfer fractional derivative with integral boundary condition.

The focus of this work is on the absolute controllability of Hilfer impulsive non-instantaneous neutral derivative (HINND) with integral boundary condition of any order. Total controllability refers to the system's ability to be controlled during the impulse time. Kuratowski measure and semigroup theory in Banach space yield the results. Furthermore, we talked about optimal controllability in conjunction with appropriate limitations. Our established outcomes are described using an example.

Mathematical study of polycystic ovarian syndrome disease including medication treatment mechanism for infertility in women.

Among women of reproductive age, PCOS (polycystic ovarian syndrome) is one of the most prevalent endocrine illnesses. In addition to decreasing female fertility, this condition raises the risk of cardiovascular disease, diabetes, dyslipidemia, obesity, psychiatric disorders and other illnesses. In this paper, we constructed a fractional order model for polycystic ovarian syndrome by using a novel approach with the memory effect of a fractional operator. The study population was divided into four groups for this reason: Women who are at risk for infertility, PCOS sufferers, infertile women receiving therapy (gonadotropin and clomiphene citrate), and improved infertile women. We derived the basic reproductive number, and by utilizing the Jacobian matrix and the Routh-Hurwitz stability criterion, it can be shown that the free and endemic equilibrium points are both locally stable. Using a two-step Lagrange polynomial, solutions were generated in the generalized form of the power law kernel in order to explore the influence of the fractional operator with numerical simulations, which shows the impact of the sickness on women due to the effect of different parameters involved.

Analysis of fractal-fractional Alzheimer's disease mathematical model in sense of Caputo derivative.

Alzheimer's disease stands as one of the most widespread neurodegenerative conditions associated with aging, giving rise to dementia and posing significant public health challenges. Mathematical models are considered as valuable tools to gain insights into the mechanisms underlying the onset, progression, and potential therapeutic approaches for AD. In this paper, we introduce a mathematical model for AD that employs the fractal fractional operator in the Caputo sense to characterize the temporal dynamics of key cell populations. This model encompasses essential elements, including amyloid-ß ($\mathbb{ A_\beta }$), neurons, astroglia and microglia. Using the fractal fractional operator, we have established the existence and uniqueness of solutions for the model under consideration, employing Leray-Schaefer's theorem and the Banach fixed-point methods. Utilizing functional techniques, we have analyzed the proposed model stability under the Ulam-Hyers condition. The suggested model has been numerically simulated by using a fractional Adams-Bashforth approach, which involves a two-step Lagrange polynomial. For numerical simulations, different ranges of fractional order values and fractal dimensions are considered. This new fractal fractional operator in the form of the Caputo derivative was determined to yield better results than an ordinary integer order. Various outcomes are shown graphically by for different fractal dimensions and arbitrary orders.

A mathematical fractal-fractional model to control tuberculosis prevalence with sensitivity, stability, and simulation under feasible circumstances.

BACKGROUND: Tuberculosis, a global health concern, was anticipated to grow to 10.6 million new cases by 2021, with an increase in multidrug-resistant tuberculosis. Despite 1.6 million deaths in 2021, present treatments save millions of lives, and tuberculosis may overtake COVID-19 as the greatest cause of mortality. This study provides a six-compartmental deterministic model that employs a fractal-fractional operator with a power law kernel to investigate the impact of vaccination on tuberculosis dynamics in a population. METHODS: Some important characteristics, such as vaccination and infection rate, are considered. We first show that the suggested model has positive bounded solutions and a positive invariant area. We evaluate the equation for the most important threshold parameter, the basic reproduction number, and investigate the model's equilibria. We perform sensitivity analysis to determine the elements that influence tuberculosis dynamics. Fixed-point concepts show the presence and uniqueness of a solution to the suggested model. We use the two-step Newton polynomial technique to investigate the effect of the fractional operator on the generalized form of the power law kernel. RESULTS: The stability analysis of the fractal-fractional model has been confirmed for both Ulam-Hyers and generalized Ulam-Hyers types. Numerical simulations show the effects of different fractional order values on tuberculosis infection dynamics in society. According to numerical simulations, limiting contact with infected patients and enhancing vaccine efficacy can help reduce the tuberculosis burden. The fractal-fractional operator produces better results than the ordinary integer order in the sense of memory effect at diffract fractal and fractional order values. CONCLUSION: According to our findings, fractional modeling offers important insights into the dynamic behavior of tuberculosis disease, facilitating a more thorough comprehension of their epidemiology and possible means of control.

Designing a novel fractional order mathematical model for COVID-19 incorporating lockdown measures.

This research focuses on the design of a novel fractional model for simulating the ongoing spread of the coronavirus (COVID-19). The model is composed of multiple categories named susceptible [Formula: see text], infected [Formula: see text], treated [Formula: see text], and recovered [Formula: see text] with the susceptible category further divided into two subcategories [Formula: see text] and [Formula: see text]. In light of the need for restrictive measures such as mandatory masks and social distancing to control the virus, the study of the dynamics and spread of the virus is an important topic. In addition, we investigate the positivity of the solution and its boundedness to ensure positive results. Furthermore, equilibrium points for the system are determined, and a stability analysis is conducted. Additionally, this study employs the analytical technique of the Laplace Adomian decomposition method (LADM) to simulate the different compartments of the model, taking into account various scenarios. The Laplace transform is used to convert the nonlinear resulting equations into an equivalent linear form, and the Adomian polynomials are utilized to treat the nonlinear terms. Solving this set of equations yields the solution for the state variables. To further assess the dynamics of the model, numerical simulations are conducted and compared with the results from LADM. Additionally, a comparison with real data from Italy is demonstrated, which shows a perfect agreement between the obtained data using the numerical and Laplace Adomian techniques. The graphical simulation is employed to investigate the effect of fractional-order terms, and an analysis of parameters is done to observe how quickly stabilization can be achieved with or without confinement rules. It is demonstrated that if no confinement rules are applied, it will take longer for stabilization after more people have been affected; however, if strict measures and a low contact rate are implemented, stabilization can be reached sooner.

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator.

In this manuscript, we developed a nonlinear fractional order Ebola virus with a novel piecewise hybrid technique to observe the dynamical transmission having eight compartments. The existence and uniqueness of a solution of piecewise derivative is treated for a system with Arzel'a-Ascoli and Schauder conditions. We investigate the effects of classical and modified fractional calculus operators, specifically the classical Caputo piecewise operator, on the behavior of the model. A model shows that a completely continuous operator is uniformly continuous, and bounded according to the equilibrium points. The reproductive number R0 is derived for the biological feasibility of the model with sensitivity analysis with different parameters impact on the model. Sensitivity analysis is an essential tool for comprehending how various model parameters affect the spread of illness. Through a methodical manipulation of important parameters and an assessment of their impact on Ro, we are able to learn more about the resiliency and susceptibility of the model. Local stability is established with next Matignon method and global stability is conducted with the Lyapunov function for a feasible solution of the proposed model. In the end, a numerical solution is derived with Newton's polynomial technique for a piecewise Caputo operator through simulations of the compartments at various fractional orders by using real data. Our findings highlight the importance of fractional operators in enhancing the accuracy of the model in capturing the intricate dynamics of the disease. This research contributes to a deeper understanding of Ebola virus dynamics and provides valuable insights for improving disease modeling and public health strategies.

Analytical investigations of propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide by three computational ideas.

This paper mainly concentrates on obtaining solutions and other exact traveling wave solutions using the generalized G-expansion method. Some new exact solutions of the coupled nonlinear Schrödinger system using the mentioned method are extracted. This method is based on the general properties of the nonlinear model of expansion method with the support of the complete discrimination system for polynomial method and computer algebraic system (AS) such as Maple or Mathematica. The nonparaxial solitons with the propagation of ultra-broad nonparaxial pulses in a birefringent optical waveguide is studied. To attain this, an illustrative case of the coupled nonlinear Helmholtz (CNLH) system is given to illustrate the possibility and unwavering quality of the strategy utilized in this research. These solutions can be significant in the use of understanding the behavior of wave guides when studying Kerr medium, optical computing and optical beams in Kerr like nonlinear media. Physical meanings of solutions are simulated by various Figures in 2D and 3D along with density graphs. The constraint conditions of the existence of solutions are also reported in detail. Finally, the modulation instability analysis of the CNLH equation is presented in detail.

A framework for the analysis of skin sores disease using evolutionary intelligent computing approach.

The most common and contagious bacterial skin disease i.e. skin sores (impetigo) mostly affects newborns and young children. On the face, particularly around the mouth and nose area, as well as on the hands and feet, it typically manifests as reddish sores. In this study, a neuro-evolutionary global algorithm is introduced to solve the dynamics of nonlinear skin sores disease model (SSDM) with the help of an artificial neural network. The global genetic algorithm is integrated with local sequential quadratic programming (GA-LSQP) to obtain the optimal solution for the proposed model. The designed differential model of skin sores disease is comprised of susceptible (S), infected (I), and recovered (R) categories. An activation function based neural network modeling is exploited for skin sores system through mean square error to achieve best trained weights. The integrated approach is validated and verified through the comparison of results of reference Adam strategy with absolute error analysis. The absolute error results give accuracy of around 10-11 to 10-5, demonstrating the worthiness and efficacy of proposed algorithm. Additionally, statistical investigations in form of mean absolute deviation, root mean square error, and Theil's inequality coefficient are exhibited to prove the consistency, stability, and convergence criteria of the integrated technique. The accuracy of the proposed solver has been examined from the smaller values of minimum, median, maximum, mean, semi-interquartile range, and standard deviation, which lie around 10-12 to 10-2.

Design of a novel intelligent computing framework for predictive solutions of malaria propagation model.

The paper presents an innovative computational framework for predictive solutions for simulating the spread of malaria. The structure incorporates sophisticated computing methods to improve the reliability of predicting malaria outbreaks. The study strives to provide a strong and effective tool for forecasting the propagation of malaria via the use of an AI-based recurrent neural network (RNN). The model is classified into two groups, consisting of humans and mosquitoes. To develop the model, the traditional Ross-Macdonald model is expanded upon, allowing for a more comprehensive analysis of the intricate dynamics at play. To gain a deeper understanding of the extended Ross model, we employ RNN, treating it as an initial value problem involving a system of first-order ordinary differential equations, each representing one of the seven profiles. This method enables us to obtain valuable insights and elucidate the complexities inherent in the propagation of malaria. Mosquitoes and humans constitute the two cohorts encompassed within the exposition of the mathematical dynamical model. Human dynamics are comprised of individuals who are susceptible, exposed, infectious, and in recovery. The mosquito population, on the other hand, is divided into three categories: susceptible, exposed, and infected. For RNN, we used the input of 0 to 300 days with an interval length of 3 days. The evaluation of the precision and accuracy of the methodology is conducted by superimposing the estimated solution onto the numerical solution. In addition, the outcomes obtained from the RNN are examined, including regression analysis, assessment of error autocorrelation, examination of time series response plots, mean square error, error histogram, and absolute error. A reduced mean square error signifies that the model's estimates are more accurate. The result is consistent with acquiring an approximate absolute error close to zero, revealing the efficacy of the suggested strategy. This research presents a novel approach to solving the malaria propagation model using recurrent neural networks. Additionally, it examines the behavior of various profiles under varying initial conditions of the malaria propagation model, which consists of a system of ordinary differential equations.

Recurrent neural network for the dynamics of Zika virus spreading.

Recurrent Neural Networks (RNNs), a type of machine learning technique, have recently drawn a lot of interest in numerous fields, including epidemiology. Implementing public health interventions in the field of epidemiology depends on efficient modeling and outbreak prediction. Because RNNs can capture sequential dependencies in data, they have become highly effective tools in this field. In this paper, the use of RNNs in epidemic modeling is examined, with a focus on the extent to which they can handle the inherent temporal dynamics in the spread of diseases. The mathematical representation of epidemics requires taking time-dependent variables into account, such as the rate at which infections spread and the long-term effects of interventions. The goal of this study is to use an intelligent computing solution based on RNNs to provide numerical performances and interpretations for the SEIR nonlinear system based on the propagation of the Zika virus (SEIRS-PZV) model. The four patient dynamics, namely susceptible patients S(y), exposed patients admitted in a hospital E(y), the fraction of infective individuals I(y), and recovered patients R(y), are represented by the epidemic version of the nonlinear system, or the SEIR model. SEIRS-PZV is represented by ordinary differential equations (ODEs), which are then solved by the Adams method using the Mathematica software to generate a dataset. The dataset was used as an output for the RNN to train the model and examine results such as regressions, correlations, error histograms, etc. For RNN, we used 100% to train the model with 15 hidden layers and a delay of 2 seconds. The input for the RNN is a time series sequence from 0 to 5, with a step size of 0.05. In the end, we compared the approximated solution with the exact solution by plotting them on the same graph and generating the absolute error plot for each of the 4 cases of SEIRS-PZV. Predictions made by the model appeared to be become more accurate when the mean squared error (MSE) decreased. An increased fit to the observed data was suggested by this decrease in the MSE, which suggested that the variance between the model's predicted values and the actual values was dropping. A minimal absolute error almost equal to zero was obtained, which further supports the usefulness of the suggested strategy. A small absolute error shows the degree to which the model's predictions matches the ground truth values, thus indicating the level of accuracy and precision for the model's output.

Qualitative analysis and chaotic behavior of respiratory syncytial virus infection in human with fractional operator.

Respiratory syncytial virus (RSV) is the cause of lung infection, nose, throat, and breathing issues in a population of constant humans with super-spreading infected dynamics transmission in society. This research emphasizes on examining a sustainable fractional derivative-based approach to the dynamics of this infectious disease. We proposed a fractional order to establish a set of fractional differential equations (FDEs) for the time-fractional order RSV model. The equilibrium analysis confirmed the existence and uniqueness of our proposed model solution. Both sensitivity and qualitative analysis were employed to study the fractional order. We explored the Ulam-Hyres stability of the model through functional analysis theory. To study the influence of the fractional operator and illustrate the societal implications of RSV, we employed a two-step Lagrange polynomial represented in the generalized form of the Power-Law kernel. Also, the fractional order RSV model is demonstrated with chaotic behaviors which shows the trajectory path in a stable region of the compartments. Such a study will aid in the understanding of RSV behavior and the development of prevention strategies for those who are affected. Our numerical simulations show that fractional order dynamic modeling is an excellent and suitable mathematical modeling technique for creating and researching infectious disease models.