A mathematical model of malaria dynamics with naturally acquired transient immunity in the presence of protected travellers is presented. The qualitative analysis carried out on the autonomous model reveals the existence of backward bifurcation, where the locally asymptotically stable malaria-free and malaria-present equilibria coexist as the basic reproduction number crosses unity. The increased fraction of protected travellers is shown to reduce the basic reproduction number significantly. Particularly, optimal control theory is used to analyse the non-autonomous model, which incorporates four control variables. The existence result for the optimal control quadruple, which minimizes malaria infection and costs of implementation, is explicitly proved. Effects of combining at least any three of the control variables on the malaria dynamics are illustrated. Furthermore, the cost-effectiveness analysis is carried out to reveal the most cost-effective strategy that could be implemented to prevent and control the spread of malaria with limited resources.

MSC Classification: 76A05; 35Q79; 80A20The present work examines the combined influence of variable thermal conductivity and viscosity on the irreversibility rate in couple stress fluid flow in between asymmetrically heated parallel plates. The dimensionless fluid equations are solved by using homotopy analysis method (HAM) and validated with Runge-Kutta shooting method (RKSM). The convergent series solution is then used for the irreversibility analysis in the flow domain. The effects of thermal conductivity and viscosity variation parameters, couple stress parameter, Reynolds number, Grashof number, Hartmann number on the velocity profile, temperature distribution, entropy production, and heat irreversibility ratio are presented through graphs, and salient features of the solutions are discussed. The computations show that the entropy production rate decreases with increased magnetic field and thermal conductivity parameters, whereas it rises with increasing values of couple stress parameter, Brinkman number, viscosity variation parameter, and Grashof number. The study is relevant to lubrication theory.

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The emission of carbon dioxide (CO2) is closely associated with oxygen (O2) depletion, and thermal decomposition in a reacting stockpile of combustible materials like fossil fuels (e.g., coal, oil, and natural gas). Moreover, it is understood that proper assessment of the emission levels provides a crucial reference point for other assessment tools like climate change indicators and mitigation strategies. In this paper, a nonlinear mathematical model for estimating the CO2emission, O2depletion, and thermal stability of a reacting slab is presented and tackled numerically using a semi-implicit finite-difference scheme. It is assumed that the slab surface is subjected to a symmetrical convective heat and mass exchange with the ambient. Both numerical and graphical results are presented and discussed quantitatively with respect to various parameters embedded in the problem.

The present article investigates the entropy generation rate in the nonlinear convective flow of a reactive couple stress liquid through a channel filled with saturated materials and subjected to convective cooling. Analytical solutions of the coupled nonlinear boundary-value problems arising from the mathematical formulation are obtained by using the Homotopy Analysis Method (HAM). The analytical solutions are further validated numerically with the fourth order Runge-Kutta (RK4) to establish the accuracy of the method. Velocity, temperature, entropy generation, and heat irreversibility ratio profiles are presented and discussed extensively. The result of the computation shows that entropy generation increases significantly with increasing buoyancy parameter.