A fractional perspective on the transmission dynamics of a parasitic infection, considering the impact of both strong and weak immunity.

Infectious disease cryptosporidiosis is caused by the cryptosporidium parasite, a type of parasitic organism. It is spread through the ingestion of contaminated water, food, or fecal matter from infected animals or humans. The control becomes difficult because the parasite may remain in the environment for a long period. In this work, we constructed an epidemic model for the infection of cryptosporidiosis in a fractional framework with strong and weak immunity concepts. In our analysis, we utilize the well-known next-generation matrix technique to evaluate the reproduction number of the recommended model, indicated by [Formula: see text]. As [Formula: see text], our results show that the disease-free steady-state is locally asymptotically stable; in other cases, it becomes unstable. Our emphasis is on the dynamical behavior and the qualitative analysis of cryptosporidiosis. Moreover, the fixed point theorem of Schaefer and Banach has been utilized to investigate the existence and uniqueness of the solution. We identify suitable conditions for the Ulam-Hyers stability of the proposed model of the parasitic infection. The impact of the determinants on the sickness caused by cryptosporidiosis is highlighted by the examination of the solution pathways using a novel numerical technique. Numerical investigation is conducted on the solution pathways of the system while varying various input factors. Policymakers and health officials are informed of the crucial factors pertaining to the infection system to aid in its control.

Fractional view analysis of sexual transmitted human papilloma virus infection for public health.

The infection of human papilloma virus (HPV) poses a global public health challenge, particularly in regions with limited access to health care and preventive measures, contributing to health disparities and increased disease burden. In this research work, we present a new model to explore the transmission dynamics of HPV infection, incorporating the impact of vaccination through the Atangana-Baleanu derivative. We establish the positivity and uniqueness of the solution for the proposed model HPV infection. The threshold parameter is determined through the next-generation matrix method, symbolized by [Formula: see text]. Moreover, we investigate the local asymptotic stability of the infection-free steady-state of the system. The existence of the solutions of the recommended model is determined through fixed-point theory. A numerical scheme is presented to visualize the dynamical behavior of the system with variation of input factors. We have shown the impact of input parameters on the dynamics of the system through numerical simulations. The findings of our investigation delineated the principal parameters exerting significant influence for the control and prevention of HPV infection.

Analytical study on couple stress flow of GO-EG and GO-W nanofluid over an extending cylinder along with variable viscosity.

The main goal of this research is to present the concept of enhancing heat transfer within emerging technology. To achieve this, tiny metal and nonmetal particles ranging from 1 to 100 nm in size are introduced into base liquids. These nanoscale particles are utilized to improve the thermal performance of the liquids, leading to what are termed nanofluids. The utilization of these fluids and the examination of the flow of thin films have valuable implications across various sectors such as engineering, technology, and industries. This research focuses on analyzing the convective flow behavior of nanofluids, specifically, graphene oxide-ethylene glycol (GO-EG) and graphene oxide-water (GO-W) on a moving surface. The study investigates the impacts of magnetic fields and varying viscosity. By making use of the thermophysical characteristics of the base fluid and the nanofluid, as well as implementing a similarity transformation within the fundamental equations that govern energy and momentum, we formulate a 5th order nonlinear ordinary differential equation (NODE) to describe the velocity profile. This is combined with a second-order NODE that describes the distribution of temperature. To solve this derived NODE, we employ a method known as the Homotopy Analysis Method (HAM) for analytical solution. The impact of the relevant factors, Prandtl number, including magnetic field parameter, thickness of the liquid, couple stress parameter, temperature distribution, dynamic viscosity, and Eckert number, on the skin friction, velocity profile, and Nusselt's number are interrogated through graphical representation. The velocity field exhibits a decline as the couple stress parameter, magnetic field parameter, liquid thickness, and dynamic viscosity experience an increase. Conversely, the temperature field displays a rise as the Eckert number and dynamic viscosity experience an increase. To ensure the convergence of the issue, dual solutions of the problem are employed, and this is verified through the utilization graphs and tables. Due to the considerable challenge encountered in heat transfer applications for cooling diverse equipment and devices across industries like automotive, microelectronics, defense, and manufacturing, there is a strong expectation that this theoretical methodology could make a favorable contribution towards enhancing heat transfer efficiency. This improvement is sought to meet the requirements of the manufacturing and engineering sectors.

Solutions of a three-dimensional multi-term fractional anomalous solute transport model for contamination in groundwater.

The study presents a meshless computational approach for simulating the three-dimensional multi-term time-fractional mobile-immobile diffusion equation in the Caputo sense. The methodology combines a stable Crank-Nicolson time-integration scheme with the definition of the Caputo derivative to discretize the problem in the temporal direction. The spatial function derivative is approximated using the inverse multiquadric radial basis function. The solution is approximated on a set of scattered or uniform nodes, resulting in a sparse and well-conditioned coefficient matrix. The study highlights the advantages of meshless method, particularly their simplicity of implementation in higher dimensions. To validate the accuracy and efficacy of the proposed method, we performed numerical simulations and compared them with analytical solutions for various test problems. These simulations were carried out on computational domains of both rectangular and non-rectangular shapes. The research highlights the potential of meshless techniques in solving complex diffusion problems and its successful applications in groundwater contamination and other relevant fields.

A fractional modeling approach for the transmission dynamics of measles with double-dose vaccination.

Measles, a member of the Paramyxoviridae family and the Morbillivirus genus, is an infectious disease caused by the measles virus that is extremely contagious and can be prevented through vaccination. When a person with the measles coughs or sneezes, the virus is disseminated by respiratory droplets. Normally, the appearance of measles symptoms takes 10-14 d following viral exposure. Conjunctivitis, a high temperature, a cough, a runny nose, and a distinctive rash are some of the symptoms. Despite the measles vaccination being available, it is still widespread worldwide. To eradicate measles, the Reproduction Number (i.e. R0<1) must remain less than unity. This study examines a SEIVR compartmental model in the caputo sense using a double dose of vaccine to simulate the measles outbreak. The reproduction number R0 and model properties are both thoroughly examined. Both the local and global stabilities of the proposed model are determined for R0 less and greater than 1. To achieve the model's global stability, the Lyapunov function is used while the existence and uniqueness of the proposed model are demonstrated In addition to the calculated and fitted biological parameters, the forward sensitivity indices for R0 are also obtained. Simulations of the proposed fractional order (FO) caputo model are performed in order to analyse their graphical representations and the significance of FO derivatives to illustrate how our theoretical findings have an impact. The graphical results show that the measles outbreak is reduced by increasing vaccine dosage rates.

Analysis of the dynamics of a vector-borne infection with the effect of imperfect vaccination from a fractional perspective.

The burden of vector-borne infections is significant, particularly in low- and middle-income countries where vector populations are high and healthcare infrastructure may be inadequate. Further, studies are required to investigate the key factors of vector-borne infections to provide effective control measure. This study focuses on formulating a mathematical framework to characterize the spread of chikungunya infection in the presence of vaccines and treatments. The research is primarily dedicated to descriptive study and comprehension of dynamic behaviour of chikungunya dynamics. We use Banach's and Schaefer's fixed point theorems to investigate the existence and uniqueness of the suggested chikungunya framework resolution. Additionally, we confirm the Ulam-Hyers stability of the chikungunya system. To assess the impact of various parameters on the dynamics of chikungunya, we examine solution pathways using the Laplace-Adomian method of disintegration. Specifically, to visualise the impacts of fractional order, vaccination, bite rate and treatment computer algorithms are employed on the infection level of chikungunya. Our research identified the framework's essential input settings for managing chikungunya infection. Notably, the intensity of chikungunya infection can be reduced by lowering mosquito bite rates in the affected area. On the other hand, vaccination, memory index or fractional order, and treatment could be used as efficient controlling variables.

Modeling and analysis of the transmission of avian spirochetosis with non-singular and non-local kernel.

An acute bacterial infection called avian spirochetosis is spread by ticks to a variety of birds. Clinical symptoms can vary greatly and are frequently non-specific. To diagnose a condition, the infectious spirochete must be detected. Here, we structure an epidemic model for the transmission of avian spirochetosis to visualize the interaction between tick and bird populations. The recommended dynamics of avian spirochetosis is illustrated with the help of fractional framework. We inspected the steady-states of the system of the avian spirochetosis for the stability analysis. The next-generation technique is used to evaluate the model's reproduction parameter R0. The infection-free and endemic steady-state of avian spirochetosis were shown to be locally asymptotically stable under the specified conditions. Through mathematical skills, the positivity of solutions is determined. Additionally, evidence supporting the existence and uniqueness of the avian spirochetosis framework solution has been shown. We conduct modified simulations of the suggested avian spirochetosis system with different input factors to study the complex phenomena of avian spirochetosis under the effect of numerous input parameters. Our outcomes illustrate the significance and plausibility of fractional parameter, and they also suggest that this input parameter may adequately account for these kinds of observations.

Mathematical study of the dynamics of lymphatic filariasis infection via fractional-calculus.

The infection of lymphatic filariasis (LF) is the primary cause of poverty and disability in individuals living with the disease. Many organizations globally are working toward mitigating the disease's impact and enhancing the quality of life of the affected patients. It is paramount to inspect the transmission pattern of this infection to provide effective interventions for its prevention and control. Here, we formulate an epidemic model for the progression process of LF with acute and chronic infection in the fractional framework. The basic concept of the novel Atangana-Baleanu operator is presented for the analysis of suggested system. We determine the basic reproduction number of the system via the approach of next-generation matrix and investigate the equilibria of the system for stability analysis. We have shown the impact of input factors on the outcomes of reproduction parameter with the help of partial rank correlation coefficient approach and visualize the most critical factors. To conceptualize the time series analysis of the suggested dynamics, we propose utilizing a numerical approach. The solution pathways of the system are illustrated to demonstrate how different settings affect the system. We demonstrate the dynamics of the infection numerically to educate the policy makers and health authorities about the mechanisms necessary for management and control.

Modeling the transmission phenomena of water-borne disease with non-singular and non-local kernel.

Drinking or recreating water that has been polluted with disease-causing organisms or pathogens is what causes waterborne infections. It should be noted that many water-borne infections can also transmit from person to person, by contact with animals or their surroundings, or by ingesting tainted food or beverages. Schistosomiasis is a water-borne infection found in different areas of the globe. Mostly people with this viral infection live in Africa with limited resources and medications. Therefore, investigation of this infection is significant to reduce its economic burden on the society. We formulated a novel epidemic model for schistosomiasis water-borne infection with the help of the Atangana-Baleanu derivative. The rudimentary theory of fractional-calculus has been presented for the analysis of our system. We start by looking at the model solution's non-negativity and uniqueness. The basic reproduction number and equilibria of the hypothesized water-borne infection model are next evaluated. Local stability of the infection-free steady-state has been established through Jacobian matrix method for R0<1. In addition, the suggested model's solution is calculated using an iterative technique. Finally, we give numerical simulations for various input values to illustrate the impact of memory index and other input factors of the system. Our findings showed the influence of input parameters on the dynamical behaviour of the schistosomiasis infection. The results demonstrate the importance and persuasive behaviour of fractional order, and reveal that fractional memory effects in the model seem to be a good fit for this type of findings.

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.

Analytical Investigation of the Time-Dependent Stagnation Point Flow of a CNT Nanofluid over a Stretching Surface.

The heat transfer ratio has an important role in industry and the engineering sector; the heat transfer ratios of CNT nanofluids are high compared to other nanofluids. This paper examines the analytical investigation of the time-dependent stagnation point flow of a CNT nanofluid over a stretching surface. For the investigation of the various physical restrictions, single and multi-walled carbon nanotubes (SWCNTs, MWCNTs) were used and compared. The defined similarity transformation was used, to reduce the given nonlinear partial differential equations (PDEs) to nonlinear ordinary differential equations (ODEs). The model nonlinear ordinary differential equations were solved, with an approximate analytical (OHAM) optimal homotopy asymptotic method being used for the model problem. The impact of different parameters such as magnetic field parameter, unsteady parameter, dimensionless nanoparticles volume friction, Prandtl number, and Eckert number are interpreted using graphs, in the form of the velocity and temperature profile.

Modeling and Analysis of Breast Cancer with Adverse Reactions of Chemotherapy Treatment through Fractional Derivative.

The abnormal growth of cells in the breast is called malignancy or breast cancer; it is a life-threatening and dangerous cancer in women around the world. In the treatment of cancer, the doctors apply different techniques to stop cancer cell development, remove cancer cells through surgery, or kill cancer cells. In chemotherapy treatment, powerful drugs are used to kill abnormal cells; however, it has adverse reactions on the patient heart which is called cardiotoxicity. In this paper, we formulate the dynamics of cancer in the breast with adverse reactions of chemotherapy treatment on the heart of a patient in the fractional framework to visualize its dynamical behaviour. We listed the fundamental results of the fractional calculus for the analysis of our model. The model is then analyzed for the basic properties, and the existence and uniqueness of the proposed breast cancer system are investigated through fixed point theory. Furthermore, the Adams-Bashforth numerical technique is presented for the solution of fractional-order system to illustrate the time series of breast cancer model. The dynamical behaviour of different stages of breast cancer is then highlighted numerically to show the effect of fractional-order ϑ and to visualize the role of input parameter on the dynamics of breast cancer.

Thermal boundary layer analysis of MHD nanofluids across a thin needle using non-linear thermal radiation.

An analysis of steady two-dimensional boundary layer MHD (magnetohydrodynamic) nanofluid flow with nonlinear thermal radiation across a horizontally moving thin needle was performed in this study. The flow along a thin needle is considered to be laminar and viscous. The Rosseland estimate is utilized to portray the radiation heat transition under the energy condition. Titanium dioxide (TiO$ _2 $) is applied as the nanofluid and water as the base fluid. The objective of this work was to study the effects of a magnetic field, thermal radiation, variable viscosity and thermal conductivity on MHD flow toward a porous thin needle. By using a suitable similarity transformation, the nonlinear governing PDEs are turned into a set of nonlinear ODEs which are then successfully solved by means of the homotopy analysis method using Mathematica software. The comparison result for some limited cases was achieved with earlier published data. The governing parameters were fixed values throughout the study, i.e., $ k_1 $ = 0.3, $ M $ = 0.6, $ F_r $ = 0.1, $ \delta_\mu $ = 0.3, $ \chi $ = 0.001, $ Pr $ = 0.7, $ Ec $ = 0.5, $ \theta_r $ = 0.1, $ \epsilon $ = 0.2, $ Rd $ = 0.4 and $ \delta_k $ = 0.1. After detailed analysis of the present work, it was discovered that the nanofluid flow diminishes with growth in the porosity parameter, variable viscosity parameter and magnetic parameter, while it upsurges when the rate of inertia increases. The thermal property enhances with the thermal conductivity parameter, radiation parameter, temperature ratio parameter and Eckert number, while it reduces with the Prandtl number and size of the needle. Moreover, skin friction of the nanofluid increases with corresponding growth in the magnetic parameter, porosity parameter and inertial parameter, while it reduces with growth in the velocity ratio parameter. The Nusselt number increases with increases in the values of the inertia parameter and Eckert number, while it decliens against a higher estimation of the Prandtl number and magnetic parameter. This study has a multiplicity of applications like petroleum products, nuclear waste disposal, magnetic cell separation, extrusion of a plastic sheet, cross-breed powered machines, grain storage, materials production, polymeric sheet, energy generation, drilling processes, continuous casting, submarines, wire coating, building design, geothermal power generations, lubrication, space equipment, biomedicine and cancer treatment.

Fractional-calculus analysis of the transmission dynamics of the dengue infection.

In this research paper, a novel approach in dengue modeling with the asymptomatic carrier and reinfection via the fractional derivative is suggested to deeply interrogate the comprehensive transmission phenomena of dengue infection. The proposed system of dengue infection is represented in the Liouville-Caputo fractional framework and investigated for basic properties, that is, uniqueness, positivity, and boundedness of the solution. We used the next-generation technique in order to determine the basic reproduction number R0 for the suggested model of dengue infection; moreover, we conduct a sensitivity test of R0 through a partial rank correlation coefficient technique to know the contribution of input factors on the output of R0. We have shown that the infection-free equilibrium of dengue dynamics is globally asymptomatically stable for R0<1 and unstable in other circumstances. The system of dengue infection is then structured in the Atangana-Baleanu framework to represent the dynamics of dengue with the non-singular and non-local kernel. The existence and uniqueness of the solution of the Atangana-Baleanu fractional system are interrogated through fixed-point theory. Finally, we present a novel numerical technique for the solution of our fractional-order system in the Atangana-Baleanu framework. We obtain numerical results for different values of fractional-order ϑ and input factors to highlight the consequences of fractional-order ϑ and input parameters on the system. On the basis of our analysis, we predict the most critical parameters in the system for the elimination of dengue infection.

Bioconvection Due to Gyrotactic Microorganisms in Couple Stress Hybrid Nanofluid Laminar Mixed Convection Incompressible Flow with Magnetic Nanoparticles and Chemical Reaction as Carrier for Targeted Drug Delivery through Porous Stretching Sheet.

In this paper, the steady electrically conducting hybrid nanofluid (CuO-Cu/blood) laminar-mixed convection incompressible flow at the stagnation-point with viscous and gyrotactic microorganisms is considered. Additionally, hybrid nanofluid flow over a horizontal porous stretching sheet along with an induced magnetic field and external magnetic field effectsthat can be used in biomedical fields, such as in drug delivery and the flow dynamics of the microcirculatory system. This investigation can also deliver a perfect view about the mass and heat transfer behavior of blood flow in a circulatory system and various hyperthermia treatments such as the treatment of cancer. The simple partial differential equations (PDEs) are converted into a series of dimensional ordinary differential equations (ODEs), which are determined using appropriate similarities variables (HAM). The influence of the suction or injection parameter, mixed convection, Prandtl number, buoyancy ratio parameter, permeability parameter, magnetic parameter, reciprocal magnetic prandtl number, bioconvection Rayleigh number, coupled stress parameter, thermophoretic parameter, Schmidt number, inertial parameter, heat source parameter, and Brownian motion parameter on the concentration, motile microorganisms, velocity, and temperature is outlined, and we study the physical importance of the present problem graphically.

Fractional Dynamics of HIV with Source Term for the Supply of New CD4+ T-Cells Depending on the Viral Load via Caputo-Fabrizio Derivative.

Human immunodeficiency virus (HIV) is a life life-threatening and serious infection caused by a virus that attacks CD4+ T-cells, which fight against infections and make a person susceptible to other diseases. It is a global public health problem with no cure; therefore, it is highly important to study and understand the intricate phenomena of HIV. In this article, we focus on the numerical study of the path-tracking damped oscillatory behavior of a model for the HIV infection of CD4+ T-cells. We formulate fractional dynamics of HIV with a source term for the supply of new CD4+ T-cells depending on the viral load via the Caputo-Fabrizio derivative. In the formulation of fractional HIV dynamics, we replaced the constant source term for the supply of new CD4+ T-cells from the thymus with a variable source term depending on the concentration of the viral load, and introduced a term that describes the incidence of the HIV infection of CD4+ T-cells. We present a novel numerical scheme for fractional view analysis of the proposed model to highlight the solution pathway of HIV. We inspect the periodic and chaotic behavior of HIV for the given values of input factors using numerical simulations.

A new model of dengue fever in terms of fractional derivative.

It is eminent that the epidemiological patterns of dengue are threatening for both the global economy and human health. The experts in the field are always in search to have better mathematician models in order to understand the transmission dynamics of epidemics models and to suggest possible control or the minimization of the infection from the community. In this research, we construct a new fractional-order system for dengue infection with carrier and partially immune classes to visualize the intricate dynamics of dengue. By using the basics of fractional theory, we determine the fundamental results of the proposed fractional-order dengue model. We obtain the basic reproduction number $R_0$ by next generation method and present the results based on it. The stability results are established for the infection-free state of the system. Moreover, sensitivity of $R_0$ is analyzed through partial rank correlation coefficient(PRCC) method to show the importance of different parameters in $R_0$. The influence of different input factors is shown on the output of basic reproduction number $R_0$ numerically. Our result showed that the threshold parameter $R_0$ can be decreased by increasing vaccination and treatment in the system. Finally, we illustrate the solution of the suggested dengue system through a numerical scheme to notice the influence of the fractional-order $\vartheta$ on the system. We observed that the fractional-order dynamics can explain the complex system of dengue infection more precisely and accurately rather than the integer-order dynamics. In addition, we noticed that the index of memory and biting rate of vector can play a significant part in the prevention of the infection.