Dengue fever is one of the most dangerous vector‐borne diseases in the world in terms of death and economic cost. Hence, the modeling of dengue fever is of great significance to understand the ...dynamics of dengue. In this paper, we extend dengue disease transmission models by including transmit vaccinated class, in which a portion of recovered individual loses immunity and moves to the susceptibles with limited immunity and hence a less transmission probability. We obtain the threshold dynamics governed by the basic reproduction number R0; it is shown that the disease‐free equilibrium is locally asymptotically stable if R0 ≤ 1, and the system is uniformly persistence if R0 > 1. We do sensitivity analysis in order to identify the key factors that greatly affect the dengue infection, and the partial rank correlation coefficient (PRCC) values for R0 shows that the bitting rate is the most effective in lowering dengue new infections, and moreover, control of mosquito size plays an essential role in reducing equilibrium level of dengue infection. Hence, the public are highly suggested to control population size of mosquitoes and to use mosquito nets. By formulating the control objective, associated with the low infection and costs, we propose an optimal control question. By the application of optimal control theory, we analyze the existence of optimal control and obtain necessary conditions for optimal controls. Numerical simulations are carried out to show the effectiveness of control strategies; these simulations recommended that control measures such as protection from mosquito bites and mosquito eradication strategies effectively control and eradicate the dengue infections during the whole epidemic.
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.
Pulse vaccination is a repeated vaccination policy, which plays a tremendous role in the global fight against communicable diseases in terms of saving medical resources and decreasing the economic ...burden. In this article, we propose a dynamic model of dengue infection with periodic transmission functions and seasonality in vector population. Furthermore, we introduce a pulse vaccination strategy in the susceptible host population to examine how frequency and intensity of implementation of this strategy affect the dynamics of dengue infection. We successfully obtained the threshold dynamics by defining the basic reproduction number R
0
, which is the spectral radius of the next generation operator and governs whether the disease dies out or not. It has been established that the infection-free periodic solution of the proposed impulsive system is globally asymptotically stable if
R
0
<
1
and is unstable otherwise. Moreover, we found that the dengue infection is uniformly persistent for the proposed system if
R
0
>
1
. Finally, we execute the system numerically to illustrate the piecewise solutions of the proposed system with impulsive vaccination measure and to investigate the influence of different control parameters on the basic reproduction. The finding indicates that a frequent implementation of the vaccination strategy with great intensity and the use of mosquito nets can essentially lead to a decline of new infections.
The behavior of hybrid nanofluid and stagnation point flow toward a stretched surface along with melting heat transfer, second-order slip, electric field, and magnetic field effect is investigated in ...this study. Hybrid nanoparticles alumina Al2O3 and copper (Cu) are considered with the base fluids water H2O. The PDEs with corresponding boundary constraints are transformed into a set of nonlinear ODEs using similarities transformation. The set of nonlinear ODEs are analyzed analytically using semianalytical method HAM in Mathematica software. Dual solution is determined which relaying on the emerging parameters included magnetic field, volume fractions, electric field, dimensionless surface velocity slip factors, Eckert number, and Prandtl number. The results are shown in the velocity and temperature curves as well as skin friction coefficient and local Nusselt number. The analysis shows that velocity profile is an increasing function of slip parameter, electric field, while reducing function of magnetic field. Temperature profile is an increasing function of magnetic field parameter, electric field parameter, volume fraction parameter, and Eckert number, while reducing function of Prandtl number. The main outcomes are as follows that hybrid nanofluids are higher thermal properties as compared to conventional fluids. As a result, hybrid nanofluid has numerous uses in engineering cosmetics, automotive industry, home industry, for cancer treatment, food packaging, pharmaceuticals, fabrics, paper plastics, paints, ceramics, food colorants, and soaps as well.
The infection of dengue is a devastating mosquito-borne infection around the globe that affects human health, social and economic sectors in low-income areas. Therefore, policymakers and health ...experts are trying to point out better policies to reduce these losses and provide better information for the development of vaccination and medication. Here, we formulated a compartmental model for the transmission phenomena of dengue fever with nonlinear forces of infection through fractional derivative. We established several results related to the solution of our dengue model by using the basic properties of fractional calculus. We determined the basic reproduction number of our fractional-order system, symbolized by
R
0
. We established the local asymptotic stability of the infection-free equilibrium of our dengue system for
R
0
<
1
, and proved that the infection-free equilibrium is globally asymptotically stable without vaccination. The threshold dynamics
R
0
is tested through partial rank correlation coefficient method to notice the importance of parameters in the transmission of dengue infection. In addition, we have shown the impact of memory on the basic reproduction number numerically with the variation of different parameters. We conclude that the biting rate, recruitment rate of mosquitoes and index of memory are the most sensitive factors, which can effectively lower the level of dengue fever. The dynamical behavior of the proposed fractional system is presented through a numerical scheme to explore the overall transmission process. We predict that the fractional-order model can explore more accurately and preciously the intricate dengue disease transmission model rather than the integer-order derivative.
Infectious diseases can have a significant economic impact, both in terms of healthcare costs and lost productivity. This can be particularly significant in developing countries, where infectious ...diseases are more prevalent, and healthcare systems may be less equipped to handle them. It is recognized that the hepatitis B virus (HBV) infection remains a critical global public health issue. In this study, we develop a comprehensive model for HBV infection that includes vaccination and hospitalization through a fractional framework. It has been shown that the solutions of the recommended system of HBV infection are positive and bounded. We examine the steady states of the model and determine the basic reproduction number; denoted by R0. The qualitative and quantitative behavior of the model is demonstrated using mathematical skills and numerical techniques. It has been proved that the infection-free steady state of the system is locally asymptotically stable if R0<1 and unstable otherwise. Furthermore, the Ulam–Hyers stability (UHS) of the recommended fractional models is investigated and the significant conditions are provided. We present an iterative technique to visualize the dynamical behavior of the system. We perform different simulations to illustrate the effect of different input factors on the solution pathways of the system of HBV infection to conceptualize the role of parameters in the control and prevention of the infection.
Farmers are trying to adopt new cultivation methods and technologies to produce more and good yield. Low productivity is due to a variety of factors; one of the main reasons is the existence of plant ...diseases spread by insects and pathogens. Infection in the plants of red chilli via the yellow virus is a current issue for the farmers. Here, we construct a model for the propagation of the yellow virus in the plants of red chilli to investigate the key factors. The proposed model is then presented in the framework of fractional derivative for more accurate findings. By applying the method of next-generation matrix, we determine the basic reproduction number
R
0
. The recommended model is investigated for biological meaningful results. Moreover, we focus on the dynamical behavior and qualitative analysis of the yellow virus infection in the plants of red chili. Schaefer and Banach fixed-point theorems are utilized to demonstrate the uniqueness and existence of the solution of the recommended system. We find suitable circumstances for the Ulam–Hyers stability of the recommended system of plants infection. The solution routes are examined using a unique numerical method to highlight the contribution of the input factors on yellow virus dynamics. Key factors of the system are investigated numerically through different simulations. The most critical factors of the infection are highlighted to the policymakers for the prevention of the losses.
The infection of human immunodeficiency virus (HIV) is a serious and potentially incurable infection. There is no cure for HIV and is a public health issue around the world. That is why, it is ...valuable to investigate the intricate phenomena of HIV infection and provide some control interventions to lessen its economic burden. In this research work, the dynamics of HIV via fractional calculus to conceptualize the intricate phenomena of this viral infection has been formulated and conceptualized. We have shown the rudimentary concept of fractional calculus in Atangana–Baleanu framework. A novel numerical technique is presented for the chaotic and dynamic behaviour of the proposed model. The oscillatory and chaotic phenomena of the system have been shown with the fluctuation of different input factors of the system. Furthermore, we have shown the affect of fractional order on the proposed system of HIV infection. Most critical input parameters are highlighted through numerical simulations and suggested control intervention to the policy makers. Finally, we have shown the stability result and the convergence condition for the proposed numerical scheme.
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 effects that 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.
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