Artificial intelligence-enhanced thermal and mass transport analysis of rotating hybrid nanofluid induced by autocatalytic reaction via MHD effects R. Surendar, Pragya Pandey, Ramesh Ramalingam, Suhas S, Prasanna Kumar Lakineni International Journal of Modeling Simulation and Scientific Computing, 2026 This work investigates the thermal and flow properties of a rotating hybrid nanofluid comprising [Formula: see text]-[Formula: see text] nanoparticles in a water-ethylene glycol matrix across a linearly extending sheet, emphasizing dissipative heat effects under magnetohydrodynamic (MHD) conditions. An essential innovation involves the amalgamation of the Fourier numerical approach with the XGBoost machine learning model to forecast and examine intricate heat and mass transfer phenomena. The model incorporates viscous and ohmic dissipation, rotational effects, and convective flow, demonstrating that ideal thermal zones can diminish hotspots by as much as 125 times, while magnetic field modulation can improve heat transfer efficiency by up to 120 times. Thorough visual assessments validate the precision of XGBoost in reproducing simulation outcomes. The novelty of this work stems from the effective fusion of machine learning with numerical simulation, providing a powerful framework for designing efficient thermal management systems in advanced engineering applications such as electronics cooling, automotive systems, and nuclear energy.
Stability and control analysis of COVID-19 spread in India using SEIR model Ramesh Ramalingam, Arul Joseph Gnanaprakasam, Salah Boulaaras Scientific Reports, 2025 In this work, we investigate a mathematical model that depicts the dynamics of COVID-19, with an emphasis on the effectiveness of detection and diagnosis procedures as well as the impact of quarantine measures. Using data from May 1 to May 31, 2020, the current study compares three states: Tamil Nadu, Maharashtra, and Andhra Pradesh. A compartmental model has been developed in order to forecast the pandemic's trajectory and devise an effective control strategy. The study then examines the dynamic progression of the pandemic by including important epidemiological factors into a modified SEIR (Susceptible, Exposed, Infectious, Recovered) model. Our method is a thorough analysis of the equilibria of the deterministic mathematical model in question. We use rigorous techniques to find these equilibrium points and then conduct a comprehensive investigation of their stability. Furthermore, an optimum control problem is applied to reduce the illness fatality, taking into account both pharmaceutical and nonpharmaceutical intervention options as control functions. With the aid of Pontryagin's maximal principle, an objective functional has been created and solved in order to minimize the number of infected people and lower the cost of the controls. In terms of the basic reproduction number, the stability of biologically plausible equilibrium points and the qualitative behavior of the model are examined. We found that the disease transmission rate has an effect on reducing the spread of diseases after conducting sensitivity analysis with regard to the basic reproduction number. According to the findings, Tamil Nadu had the lowest reproduction number ([Formula: see text]) and Maharashtra the highest ([Formula: see text]), indicating regional differences in the efficacy of public health initiatives. Furthermore, it has been demonstrated that appropriate control strategies, such as vaccination (Μ), can successfully reduce infection levels and improve recovery rates. In our study compared to the other two states, Tamil Nadu is notable for its quick recovery and decrease in infection rates. In our findings are more dependable and applicable when mathematical analysis and numerical simulations are combined, which also helps to provide a more thorough understanding of the dynamics at work in the COVID-19 environment. This research also offers suggestions for how government agencies, health groups, and legislators can lessen the effects of COVID-19 and distribute resources as efficiently as possible . Finally, we conclude by discussing the optimal control strategy to contain the epidemic.
Optimal Control Strategies for COVID-19 Epidemic Management: A Mathematical Modeling Approach Using the SEIQR Framework R. Ramalingam, A. Gnanaprakasam, S. Boulaaras Revista Internacional De Metodos Numericos Para Calculo Y Diseno En Ingenieria, 2025 The COVID-19 pandemic has necessitated the development of robust mathematical models to understand and mitigate its impact. This study presents a compartmental model for the Indian pandemic COVID-19 dynamics, incorporating key compartments such as susceptible, exposed, infected, quarantined, and recovered populations. The positivity and boundedness of solutions are rigorously analyzed to ensure that the model remains biologically meaningful over time. A detailed exploration of the basic reproduction number R0 is conducted using the next-generation matrix approach, identifying it as a pivotal threshold parameter dictating disease dynamics. The equilibria of the system, including the Disease-Free Equilibrium (DFE) and the Endemic Equilibrium (EE), are derived and analyzed for their stability properties. The local stability of the DFE is established for R0 < 1, while conditions for the existence and stability of the EE are explored for R0 > 1. Additionally, the study employs Lyapunov functions to assess the global stability of equilibria, ensuring the robustness of the proposed model under varying initial conditions. The Pontryagin’s Maximum Principle is utilized to derive optimal control strategies, focusing on minimizing the number of infections and optimizing interventions such as vaccination, treatment, and quarantine measures like wearing a face mask and hand washing. Numerical simulations validate the theoretical findings, providing critical insights into the effectiveness of various control measures. This comprehensive framework contributes to the mathematical understanding of COVID-19 dynamics and offers valuable guidance for public health decision-making.
The Optimal Control Methods for the Covid-19 Pandemic Model’s Precise and Practical SIQR Mathematical Model Iaeng International Journal of Applied Mathematics, 2024
Approximate solutions of viral dynamics in HBV infection using homotopy perturbation method S. Balamuralitharan, R. Ramesh Aip Conference Proceedings, 2020 This paper deals the HBV infections using Homotopy Perturbation Method, Using Mathematical modeling for the three compartments such as T, I and V Where T denotes the target uninfected cells, I denotes infected cells, V denotes Hepatitis B virus in the dynamic models also Considering that β is the rate of target uninfected cells gets infected, and this happens when the target uninfected cells and virus interact with each other. Assuming that δ is the death rate of infected liver cells, and α is the production rate of virus. c is the death of virus. The new target cells are produced at the constant rate s and the target cells dies before getting infected at the rate dT and it’s the natural death, α, β , δ, c, s & d these six parameters estimations through the viral dynamics V, Homotopy Perturbation Method is used to derive the approximate solutions of the Nonlinear Differential Equation systems, The numerical solutions carried out from the MATLAB programme.
