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In this study, a new deterministic mathematical model based on fractional-order derivative operator that describes the pseudo-recovery dynamics of an epidemiological process is developed. Fractional-order derivative of Caputo type is used to examine the effect of memory in the spread process of infectious diseases with pseudo-recovery. The well-posedness of the model is qualitatively investigated through Banach fixed point theory technique. The spread of the disease in the population is measured by analysing the basic reproduction of the model with respect to its parameters through the sensitivity analysis. Consequently, the analysis is extended to the fractional optimal control model where time-dependent preventive strategy and treatment measure are characterized by Pontryagin’s maximum principle. The resulting Caputo fractional-order optimality system is simulated to understand how both preventive and treatment controls affect the pseudo-recovery dynamics of infectious diseases in the presence of memory. Graphical illustrations are shown to corroborate the qualitative results, and to demonstrate the importance of memory effects in infectious disease modelling. It is shown that time-dependent preventive strategy and treatment measure in the presence of memory engenders significant reduction in the spread of the disease when compared with memoryless situation.

A mathematical investigation of a thermodynamical system linked with energy management and its impact on the environment, especially climate change, is presented in this study. In this regard, a numerical investigation of the flow and heat transfer of hydromagnetic third-grade liquid through a porous medium. The permeability of the medium and electrical conductivity of the fluid are assumed to be temperature functions. The appropriate mathematical formulations for momentum, energy, and entropy equations are presented in both dimensional and dimensionless forms. We obtained the numerical solutions using the spectral version of the Chebyshev collocation method and compared the result with the shooting Runge–Kutta method. Numerical results for velocity, temperature, entropy, and Bejan profiles are communicated through tables and graphs with adequate physical interpretation. The thermal stability of the thermo-fluid system that guarantees the prevention of spontaneous fluid heating that fuels climate change is also included in the analysis.

In this work, the population dynamics of psychoactive substance abuse model governed by a system of nonlinear ordinary differential equations is studied through the efficacy and economic analyses. The study considers three time‐variant intervention strategies, such as screening of addicted immigrants, advocacy against substance abuse and rehabilitation therapy for the control of substance abuse spread in the population. Most sensitive parameters to be targeted by the control interventions are examined through sensitivity analysis using the normalized forward sensitivity index. By employing optimal control theory, the existence of optimal control is qualitatively analysed and the control triple is characterized using Pontryagin’s maximum principle. To further assess the impact of the intervention strategies, three different policies combining any two of the intervention strategies, namely, Policy A (combination of screening of addicted immigrants and advocacy against substance abuse), Policy B (combination of screening of addicted immigrants and rehabilitation therapy) and Policy C (combination of advocacy against substance abuse and rehabilitation therapy), are considered. Efficacy and economic analyses are extensively conducted on each of the policies, and it is revealed that Policy B is the most efficient intervention, while Policy C is the most cost‐effective intervention. As a result, the policy that averts the highest number of psychoactive substance abuse cases when limited resources are available is recommended.

Despite the wide application of combustion in reactive materials, one of the challenges faced globally is the auto-ignition of such materials, resulting in fire and explosion hazards. To avoid this unfortunate occurrence, a mathematical model describing the thermal decomposition of combustible polymer material in a rectangular stockpile is formulated. A nonlinear momentum equation is provided with the assumption that the combustible polymer follows a Carreau constitutive relation. The chemical reaction of the polymer material is assumed to be exothermic; therefore, Arrhenius’s kinetic theory is considered in the energy balance equation. The bivariate spectral local linearization scheme (BSLLS) is utilized to provide a numerical solution for the dimensionless equations governing the problem. The obtained results are validated by the collocation weighted residual method (CWRM), and a good agreement is achieved. Dimensionless velocity, temperature, and thermal stability results are presented and explained comprehensively with suitable applications. Some of the obtained results show that thermal criticality increases with increasing power law index (n) and radiation (Ra) values and decreases with increasing variable viscosity (β1) and material parameter (We) values.

This study presents a mathematical analysis of the collective effect of chemical reactions, variable fluid properties, and thermal stability of a hydromagnetic couple-stress fluid flowing through a microchannel driven by electro-osmosis and a pressure gradient. The viscosity of the biofluid is assumed to depend on the temperature, while the electrical conductivity is assumed to be a linear function of the drift velocity. The governing equations are derived non-dimensionalized, and numerical solutions are obtained using the spectral Chebyshev collocation method. The numerical solution is validated using the shooting Runge–Kutta method. The effects of varying the parameters on the thermal stability, temperature, velocity, and entropy profiles are discussed with adequate interpretations using tables and graphs. The results reveal that the chemical reactions and viscosity parameter increase the fluid temperature, while the Hartmann number decreases the temperature and increases the flow velocity and entropy generation. It was also observed that the chemical reactions and viscosity parameter increased the entropy at the channel walls, while the Hartmann number decreased the entropy at the core center of the channel. This study has tremendous empirical significance, including but not limited to biophysical applications of devices, engineering applications such as control systems, and thermo-fluidic transport.

In this study, a mathematical model for the transmission dynamics of malaria among different socioeconomic groups in the human population interacting with a susceptible-infectious vector population is presented and analysed using a fractional-order derivative of the Caputo type. The total human population is stratified into two distinguished classes of lower and higher income individuals, with each class further subdivided into susceptible, infectious, and recovered populations. The socio hierachy-structured fractional-order malaria model is analyzed through the application of different dynamical system tools. The theory of positivity and boundedness based on the generalized mean value theorem is employed to investigate the basic properties of solutions of the model, while the Banach fixed point theory approach is used to prove the existence and uniqueness of the solution. Furthermore, unlike the existing related studies, comprehensive global asymptotic dynamics of the fractional-order malaria model around both disease-free and endemic equilibria are explored by generalizing the usual classical methods for establishing global asymptotic stability of the steady states. The asymptotic behavior of the trajectories of the system are graphically illustrated at different values of the fractional (noninteger) order.

A numerical investigation into the effect of temperature-dependent fluid properties on the thin film flow along an inclined heated plate is presented. The equations governing the coupled flow and heat transfer are formulated based on couple stress non-Newtonian model. Solutions of the coupled nonlinear differential equations are tackled numerically by using the combination of shooting method and the Fehlberg-Runge-Kutta method. Findings are presented graphically and discussed precisely.

This qualitative study aimed to identify the optimal formula for attaining organisational excellence by integrating quantitative performance measurements with a commitment to employee wellbeing. The article, grounded in comprehensive research from academic databases and industry publications, challenges the prevalent notion that high performance is the sole criterion for achieving exceptional performance. The study's results indicate that organisations can cultivate a culture of continuous improvement and achieve exceptional performance by adopting a balanced strategy that integrates high standards with empathetic and considerate leadership. Rigour in organisations is delineated, along with its components and the implications for operational efficiency and quality assurance. Moreover, the study elucidates how the application of data analysis and analytical tools can enhance an organisation's strategic performance. The significance of compassion is elucidated, along with its beneficial impact on fostering a pleasant work atmosphere characterised by empathy and emotional intelligence. The article further explores the convergence of rigour and compassion, identifying potential methods for attaining equilibrium. Additionally, it discusses the proposed theoretical foundations for the model, the measuring instruments, and the implementation plans, which encompass training and successful change management. Furthermore, identified research gaps are examined, along with the consequences of the findings for managers and leaders, and recommendations for organisations aiming for excellence are emphasised. The study ultimately indicates that sustainable success or excellence is attainable just through the integration of rigour and compassion, which would significantly affect stakeholders. This research advocates a transformation in organisational cultures and urges businesses to abandon the myth of the merciless high performance to facilitate enhanced innovation, commitment, and achievement.