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Variable viscosity, activation energy and microgravity effects on Darcy nanofluid for the thermal performance improvement in thermal energy storage systems through stretching flat plate solar collector is the focus of this research. Thermal energy storage (TES) can be improved though solar collectors, phase change materials and photovoltaic cells using nanofluid in the base liquid. To increase the reaction rate in nanoparticles, the activation energy and solar radiations are used for the efficiency of TES. The viscosity of nanofluid improves the heat and mass transmission. Due to solar radiations, nanofluid plays prominent role in TES applications such as heat exchangers, electronic cooling devices and solar power generation through solar plate collector. Solar energy based mathematical model is developed to execute the frequency of oscillating heat transfer in TES numerically. Primitive and Stokes coefficients are used for feasible programming. Finite difference analysis is performed to display oscillatory thermal energy using Gaussian-elimination matrix scheme. Steady velocity, surface temperature and concentrations are plotted and utilized in oscillatory formula to perform oscillatory skin friction, oscillatory heat transfer and oscillatory mass transfer along π⁄4 angle. Fluid velocity enhances but temperature and concentration variation decreases as viscosity decreases. High amplitude in velocity, temperature and concentration is sketched as activation energy and microgravity increases. Steady heat and mass transmission enhances as thermophoretic and Brownian motion enhances. Amplitude and frequency of oscillations in heat transport, skin friction and mass transport enhances as Prandtl and Schmidt component enhances. In validation of results, the 0.00064% percentage error for heat transport and 0.00102% percentage error for mass transmission are deduced., (© 2024. The Author(s).)

Faba bean is one of the most important grown plants worldwide for human and animal. Despite its various importance, the productivity of faba bean has been constrained by several biotic and abiotic factors. Many faba bean pathogens have been reported so far, of which the most important yield limiting disease is Chocolate Spot Disease (Botrytis fabae). The dynamics of disease transmission and decision-making processes for intervention programs for disease control are now better understood through the use of mathematical modeling. In this paper a deterministic mathematical model for Chocolate Spot disease (CSD) on faba bean plant with an optimal control model was developed and analyzed to examine the best strategy in controlling CSD. The optimal control model is developed with three control interventions, namely prevention ( u 1 ), quarantine ( u 2 ) and chemical control ( u 3 ). The Pontryagin'€™s maximum principle isused to derive the Hamiltonian, the adjoint variables, the characterization of the controls and the optimality system. A cost-effective approach is chosen from a set of possible integrated strategies using the incremental cost-effectiveness ratio (ICER). The forward-backward sweep iterative approach is used to run numerical simulations. We obtained the Hamiltonian, the adjoint variables, the characterization of the controls and the optimality system. The numerical results demonstrate that each integrated strategy can reduce the diseases within the specified period. However due to limited resources, an integrated strategy prevention and uprooting was found to be a best cost-effective strategy to combat CSD. Therefore, attention should be given for the integrated cost-effective and environmentally eco-friendly strategy by stake holders and policy makers to control CSD and disseminate the integrated intervention to the farmers in order to fight the spread of CSD in the Faba bean population and produce the expected yield from the field., (© 2024. The Author(s).)

This study proposes a non-linear mathematical model for analysing the effect of COVID-19 dynamics on the student population in higher education institutions. The theory of positivity and boundedness of solution is used to investigate the well-posedness of the model. The disease-free equilibrium solution is examined analytically. The next-generation operator method calculates the basic reproduction number ( R 0 ) . Sensitivity analyses are carried out to determine the relative importance of the model parameters in spreading COVID-19. In light of the sensitivity analysis results, the model is further extended to an optimal control problem by introducing four time-dependent control variables: personal protective measures, quarantine (or self-isolation), treatment, and management measures to mitigate the community spread of COVID-19 in the population. Simulations evaluate the effects of different combinations of the control variables in minimizing COVID-19 infection. Moreover, a cost-effectiveness analysis is conducted to ascertain the most effective and least expensive strategy for preventing and controlling the spread of COVID-19 with limited resources in the student population., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2023 The Author(s).)

This paper examines the flow structure and heat transfer characteristics of a reactive variable viscosity polyalphaolefin (PAO)-based nanolubricant containing titanium dioxide (TiO 2 ) nanoparticles in a microchannel. The nonlinear model equations are obtained and numerically solved via the shooting method with Runge-Kutta-Fehlberg integration scheme. Pertinent results depicting the effects of emerging thermophysical parameters on the reactive lubricant velocity, temperature, skin friction, Nusselt number and thermal stability criteria are presented graphically and discussed. It is found that the Nusselt number and thermal stability of the flow process improve with exothermic chemical kinetics, Biot number, and nanoparticles volume fraction but lessen with a rise in viscous dissipation and activation energy.

A numerical investigation of MHD blood flow through a stenosed permeable curved artery has been done in this study. Blood flow is considered in two-phases; core and plasma region, respectively. Viscosity of the core region is considered as temperature-dependent, while constant viscosity is considered in plasma region. The governing equations of the proposed two-phase blood flow model are considered in the toroidal coordinate system. The second-order finite difference method is adopted to solve governing equations with [Formula: see text] tolerance in the iteration process. A comparative study of Darcy number (Da) is performed to understand the influence of permeable and impermeable wall conditions. The effect of various physical parameters such as magnetic field (M), viscosity variation parameter ([Formula: see text]), Darcy number (Da), heat source (H) and chemical reaction parameter ([Formula: see text]) is displayed graphically on the flow velocity, temperature, concentration, wall shear stress and frictional resistance profiles. A comparison with published work has also been displayed through the graph to validate the present model, and it is in fair agreement with the existing work. The present study suggested that the curvature and permeability of the arterial wall raise the risk of atherosclerosis formation, while the implication of heat source on the blood flow lower this risk., (© 2022. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.)

This paper focuses on a mathematical model for coffee berry disease infestation dynamics. This model considers coffee berry and vector populations with the interaction of fungal pathogens. In order to gain an insight into the global dynamics of coffee berry disease transmission and eradication on any given coffee farm, the assumption of logistic growth with a carrying capacity reflects the fact that the amount of coffee plants depends on the limited size of the coffee farm. First, we show that all solutions of the chosen model are bounded and non-negative with positive initial data in a feasible region. Subsequently, endemic and disease-free equilibrium points are calculated. The basic reproduction number with respect to the coffee berry disease-free equilibrium point is derived using a next generation matrix approach. Furthermore, the local stability of the equilibria is established based on the Jacobian matrix and Routh Hurwitz criteria. The global stability of the equilibria is also proved by using the Lyapunov function. Moreover, bifurcation analysis is proved by the center manifold theory. The sensitivity indices for the basic reproduction number with respect to the main parameters are determined. Finally, the numerical simulations show the agreement with the analytical results of the model analysis.

Nanofluids have great potential due to their improved properties that make them useful for addressing various industrial and engineering problems. In order to use nanofluids on an industrial scale, it is first important to discuss their rheological behavior in relation to heat transfer aspects. In the current study, the flow characteristics of nanofluids are discussed using a mathematical model that is developed by fundamental laws and experimental data. The data are collected in the form of viscosity versus shear rate for different homogeneous ethylene glycol- (EG) based nanofluids, which are synthesized by dispersing 5-20% nanoparticle concentrations of SiO 2 , MgO, and TiO 2 with diameters of (20-30 nm, 60-70 nm), (20 nm, 40 nm), and (30 nm, 50 nm), respectively. The data are fitted into a rheological power-law model and further used to govern equations of a physical problem. The problem is simplified into ordinary differential equations by using a boundary layer and similarity transformations and then solved through the numerical Runge-Kutta (RK) method. The obtained results in the form of velocity and temperature profiles at different nanoparticle concentrations and diameters are displayed graphically for discussion. Furthermore, displacement and momentum thicknesses are computed numerically to explain boundary-layer growth. The results show that the velocity profile is reduced and the temperature profile is raised by increasing the nanoparticle concentration. Conversely, the velocity profile is increased and the temperature profile is decreased by increasing the nanoparticle diameter. The results of the present investigation regarding heat and mass flow behavior will help engineers design equipment and improve the efficacy and economy of the overall process in the industry.

A nonlinear differential equation model is proposed to study the dynamics of HIV/AIDS and its effects on workforce productivity. The disease-free equilibrium point of the model is shown to be locally asymptotically stable when the associated basic reproduction number [Formula: see text] is less than unity. The model is also shown to exhibit multiple endemic states for some parameter values when [Formula: see text] and [Formula: see text]. Global asymptotic stability of the disease-free equilibrium is guaranteed only when the fractions of the Susceptible subclass populations are within some bounds. Optimal control analysis of the model revealed that the most cost effective strategy that should be adopted in the fight against HIV/AIDS spread within the workforce is one that seeks to prevent infections and the treatment of infected individuals., (© 2021. Springer Nature B.V.)

Background: The present work provides important insights regarding three dimensional unsteady magnetohydrodynamic flow and entropy generation of micropolar Casson Cross nanofluid subject to nonlinear thermal radiation and chemical reaction. The Buongiorno's nanofluid model featured with Brownian movement and thermophoresis is considered. Realistic aspects namely convective boundary condition, viscous dissipation and joule heating are introduced. The present problem is modeled by momentum, temperature, microrotation and nanoparticles concentration equations., Method: The non-dimensional highly nonlinear differential equations are solved numerically via shooting iteration technique together with 4th order Runge-Kutta integration scheme., Results: The current study imparts a reasonable, pragmatic and realistic approach to a good absorber of solar energy. In addition, strong and visionary profiles of velocity, microrotation, temperature, nanoparticles concentration, entropy generation rate and Bejan number for concern nanofluids are presented. Besides, intensive physical interpretation of the involved thermophycal parameters has been well-addressed., Conclusions: The present investigation shows that strengthening of Weissenberg number uplifts the axial as well transverse fluid velocities while that of Hartmann number turns out to be a reverse trend. Furthermore, heat and mass transfer rates exhibit ascending and descending trends for intensified Brownian motion and thermophoresis respectively. Improved thermal boundary layer due to the upgrading temperature ratio parameter is another outcome of the current analysis., Competing Interests: Declaration of Competing Interest None., (Copyright © 2019. Published by Elsevier B.V.)

Measles is an awfully contagious acute viral infection. It can be fatal, causing cough, red eyes, followed by a fever and skin rash with signs of respiratory infection. In this paper, we propose and analyze a model describing the transmission dynamics of a measles epidemic in the human population using the stability theory of differential equations. The model proposed undergoes a backward bifurcation for some parameter values. Sensitivity analysis is carried out on the model parameters in order to determine their impact on the disease dynamics. We extend the model to an optimal control problem by including time-dependent control variables: prevention, treatment of infected people and vaccination of the susceptible humans. In an attempt to minimize the infected people and the cost applied we design the cost functional. Next, we show that optimal control exists for the system, and the Pontryagin maximum principle is employed to characterize the continuous controls. Numerical simulation is performed to justify the analytical results and discussed quantitatively., (Copyright © 2020. Published by Elsevier B.V.)

In this paper, the dysentery dynamics model with controls is theoretically investigated using the stability theory of differential equations. The system is considered as SIRSB deterministic compartmental model with treatment and sanitation. A threshold number R 0 is obtained such that R 0 ≤   1 indicates the possibility of dysentery eradication in the community while R 0 > 1 represents uniform persistence of the disease. The Lyapunov-LaSalle method is used to prove the global stability of the disease-free equilibrium. Moreover, the geometric approach method is used to obtain the sufficient condition for the global stability of the unique endemic equilibrium for R 0 > 1 . Numerical simulation is performed to justify the analytical results. Graphical results are presented and discussed quantitatively. It is found out that the aggravation of the disease can be decreased by using the constant controls treatment and sanitation.

In this paper, a deterministic compartmental eco- epidemiological model with optimal control of Newcastle disease (ND) in Tanzania is proposed and analysed. Necessary conditions of optimal control problem were rigorously analysed using Pontryagin's maximum principle and the numerical values of model parameters were estimated using maximum likelihood estimator. Three control strategies were incorporated such as chicken vaccination (preventive), human education campaign and treatment of infected human (curative) and its' impact were graphically observed. The incremental cost effectiveness analysis technique used to determine the most cost effectiveness strategy and we observe that combination of chicken vaccination and human education campaign strategy is the best strategy to implement in limited resources. Therefore, ND can be controlled if the farmers will apply chicken vaccination properly and well in time.

We propose and analyse a nonlinear mathematical model for the transmission dynamics of pneumonia disease in a population of varying size. The deterministic compartmental model is studied using stability theory of differential equations. The effective reproduction number is obtained and also the asymptotic stability conditions for the disease free and as well as for the endemic equilibria are established. The possibility of bifurcation of the model and the sensitivity indices of the basic reproduction number to the key parameters are determined. Using Pontryagin's maximum principle, the optimal control problem is formulated with three control strategies: namely disease prevention through education, treatment and screening. The cost-effectiveness analysis of the adopted control strategies revealed that the combination of prevention and treatment is the most cost-effective intervention strategies to combat the pneumonia pandemic. Numerical simulation is performed and pertinent results are displayed graphically.

We propose and analyze a compartmental nonlinear deterministic mathematical model for the typhoid fever outbreak and optimal control strategies in a community with varying population. The model is studied qualitatively using stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. The model exhibits a forward transcritical bifurcation and the sensitivity analysis is performed. The optimal control problem is designed by applying Pontryagin maximum principle with three control strategies, namely, the prevention strategy through sanitation, proper hygiene, and vaccination; the treatment strategy through application of appropriate medicine; and the screening of the carriers. The cost functional accounts for the cost involved in prevention, screening, and treatment together with the total number of the infected persons averted. Numerical results for the typhoid outbreak dynamics and its optimal control revealed that a combination of prevention and treatment is the best cost-effective strategy to eradicate the disease.

In this paper, a nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics and effects of HIV-malaria co-infection in the workplace. Basic reproduction numbers of sub-models are derived and are shown to have LAS disease-free equilibria when their respective basic reproduction numbers are less than unity. Conditions for existence of endemic equilibria of sub-models are also derived. Unlike the HIV-only model, the malaria-only model is shown to exhibit a backward bifurcation under certain conditions. Conditions for optimal control of the co-infection are derived using the Pontryagin's maximum principle. Numerical experimentation on the resulting optimality system is performed. Using the incremental cost-effectiveness ratio, it is observed that combining preventative measures for both diseases is the best strategy for optimal control of HIV-malaria co-infection at the workplace.

In this paper we formulate a mathematical model for malaria-cholera co-infection in order to investigate their synergistic relationship in the presence of treatments. We first analyze the single infection steady states, calculate the basic reproduction number and then investigate the existence and stability of equilibria. We then analyze the co-infection model, which is found to exhibit backward bifurcation. The impact of malaria and its treatment on the dynamics of cholera is further investigated. Secondly, we incorporate time dependent controls, using Pontryagin's Maximum Principle to derive necessary conditions for the optimal control of the disease. We found that malaria infection may be associated with an increased risk of cholera but however, cholera infection is not associated with an increased risk for malaria. Therefore, to effectively control malaria, the malaria intervention strategies by policy makers must at the same time also include cholera control., (Copyright © 2014 Elsevier Inc. All rights reserved.)

A nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics of HIV/AIDS in the workplace. The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number, ℛ0, is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated when ℛ0 < 1, whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin's Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.

We examine the effect of magnetic field on boundary layer flow of an incompressible electrically conducting water-based nanofluids past a convectively heated vertical porous plate with Navier slip boundary condition. A suitable similarity transformation is employed to reduce the governing partial differential equations into nonlinear ordinary differential equations, which are solved numerically by employing fourth-order Runge-Kutta with a shooting technique. Three different water-based nanofluids containing copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are taken into consideration. Graphical results are presented and discussed quantitatively with respect to the influence of pertinent parameters, such as solid volume fraction of nanoparticles (φ), magnetic field parameter (Ha), buoyancy effect (Gr), Eckert number (Ec), suction/injection parameter (f w ), Biot number (Bi), and slip parameter ( β ), on the dimensionless velocity, temperature, skin friction coefficient, and heat transfer rate.

The thermodynamic second law analysis is utilized to investigate the inherent irreversibility in an unsteady hydromagnetic generalized Couette flow with variable electrical conductivity in the presence of induced electric field. Based on some simplified assumption, the model nonlinear governing equations are obtained and solved numerically using semidiscretization finite difference techniques. Effects of various thermophysical parameters on the fluid velocity, temperature, current density, skin friction, the Nusselt number, entropy generation number, and the Bejan number are presented graphically and discussed quantitatively.

The aim of this paper is to analyze the recruitment effects of susceptible and infected individuals in order to assess the productivity of an organizational labor force in the presence of HIV/AIDS with preventive and HAART treatment measures in enhancing the workforce output. We consider constant controls as well as time-dependent controls. In the constant control case, we calculate the basic reproduction number and investigate the existence and stability of equilibria. The model is found to exhibit backward and Hopf bifurcations, implying that for the disease to be eradicated, the basic reproductive number must be below a critical value of less than one. We also investigate, by calculating sensitivity indices, the sensitivity of the basic reproductive number to the model's parameters. In the time-dependent control case, we use Pontryagin's maximum principle to derive necessary conditions for the optimal control of the disease. Finally, numerical simulations are performed to illustrate the analytical results. The cost-effectiveness analysis results show that optimal efforts on recruitment (HIV screening of applicants, etc.) is not the most cost-effective strategy to enhance productivity in the organizational labor force. Hence, to enhance employees' productivity, effective education programs and strict adherence to preventive measures should be promoted.

In this paper, a deterministic malaria transmission model in the presence of a drug-resistant strain is investigated. The model is studied using stability theory of differential equations, optimal control, and computer simulation. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved in the absence of a drug-resistant strain in the population. The existence of multiple endemic equilibria is also established. Both the Sensitivity Index (SI) of the model parameters and the Incremental Cost-Effectiveness Ratio (ICER) for all possible combinations of the disease-control measures are determined. Our results revealed among others that the most cost-effective strategy for drug-resistant malaria control is the combination of the provision of basic amenities (such as access to clean water, electricity, good roads, health care, and education) and treatment of infective individuals. Therefore, more efforts from policy-makers on the provisions of basic amenities and treatment of infectives would go a long way to combat the malaria epidemic.

We derived and analyzed rigorously a mathematical model that describes the dynamics of malaria infection with the recruitment of infected immigrants, treatment of infectives and spray of insecticides against mosquitoes in the population. Both qualitative and quantitative analysis of the deterministic model are performed with respect to stability of the disease free and endemic equilibria. It is found that in the absence of infected immigrants disease-free equilibrium is achievable and is locally asymptotically stable. Using Pontryagin's Maximum Principle, the optimal strategies for disease control are established. Finally, numerical simulations are performed to illustrate the analytical results., (Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.)