A non-linear mathematical model for analysing the impact of COVID-19 disease on higher education in developing countries.

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 (R0). 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.

Hemodynamical analysis of MHD two phase blood flow through a curved permeable artery having variable viscosity with heat and mass transfer.

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.

Mathematical Analysis of an Industrial HIV/AIDS Model that Incorporates Carefree Attitude Towards Sex.

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.

Entropy optimized MHD 3D nanomaterial of non-Newtonian fluid: A combined approach to good absorber of solar energy and intensification of heat transport.

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.

A co-infection model of malaria and cholera diseases with optimal control.

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.

Numerical investigation of entropy generation in unsteady MHD generalized Couette flow with variable electrical conductivity.

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.

Impact of chemo-therapy on optimal control of malaria disease with infected immigrants.

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.