Dissertations/Theses - Department of Mathematics

Browse

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    Dynamic optimization technique to reduce the health complexity of covid-19 Co-infection with severe diseases
    (Department of Mathematics, BUET, 2025-01-19) Abdul Hye, Md.; Forhad Uddin, Dr. Mohammed
    This research presents a comprehensive study of the transmission dynamics and control strategies for co-infections involving COVID-19 and other significant health conditions, using advanced mathematical modeling. Existing research on COVID- 19 transmission has primarily focused on single-disease models and standard com- partmental frameworks, leaving critical gaps in understanding how co-infections evolve and how best to manage them.To address this shortfall, the thesis investi- gates COVID-19 co-infections with severe diseases such as dengue, diabetes, kidney disease, and lung cancer, introducing four distinct yet interrelated models. These models extend traditional SIR-based approaches by integrating Pontryagin’s Max- imum Principle to derive optimal control measures, incorporating real-world data, and adopting a hybrid Bayesian–least squares and root mean square error parame- ter estimation technique for rigorous calibration. Such methodological innovations tackle recognized research gaps, including the scarcity of analytical and numerical studies on the interplay between COVID-19 and other diseases, the limited ex- ploration of vaccination and targeted treatments in dual-disease contexts, and the underutilization of advanced optimization methods in epidemiological models.By analyzing basic reproduction numbers, equilibrium points, and stability conditions for each co-infection, the thesis demonstrates that comprehensive interventions— such as public health education, specialized treatment protocols, early screening, targeted chemotherapy, and vaccination—significantly reduce infection rates. The findings underscore that implementing optimal control measures significantly re- duces co-infected cases, supporting strategic interventions to mitigate COVID-19 and dengue’s impact. Results show that vaccination substantially lowers the inci- dence of COVID-19 and its co-infections with diabetes. The model offers crucial insights into the role of vaccination in mitigating disease spread among diabetic populations and lays the groundwork for developing targeted disease control strate- gies. Furthermore, the findings demonstrate that applying these controls collectively can significantly reduce co-infection rates, underscoring the necessity of integrated healthcare solutions.Moreover, the pioneering model examining the intersection of COVID-19 and lung cancer offers an innovative perspective on how co-infections exacerbate disease burdens, emphasizing that combined strategies can guide popu- lations toward a disease-free equilibrium. Overall, this research not only enhances the theoretical understanding of multi-disease dynamics but also provides action- able insights for policymakers and healthcare professionals, illustrating that strate- gic, data-driven interventions can substantially mitigate the global impact of the COVID-19 pandemic and reduce the risks posed by concurrent illnesses. Finally, this study provides a robust mathematical foundation for understanding and controlling the dynamics of COVID-19 co-infections with severe disease. The insights and strategies developed herein aim to inform public health policies and optimize intervention approaches, contributing to the global effort to mitigate the impact of the COVID-19 pandemic.
  • Thumbnail Image
    Item
    Solution behaviour of flow in a non-aligned straight rotating pipe and across (cross flow over) a horizontal cylinder
    (Department of Mathematics, BUET, 2005-01) Abdul Hye, Md.; Khan, Dr. Md. Abdul Hakim
    In thIS thesis under lhe title "Solution behaviour of flow in a non-aligned straight rotating pipe and across (cross flow over) a horizontal cylinder", we have studied two problems namely dominant singularity behaviour of flow in a non-aligned straight rotating pIpe and conjugate effects of heat and mass transfer on natural convection flow across an isothermal horizontal circular cylinder with chemical reaction, which belong to two different realms, Firstly, we have studied the flow in a non-aligned straight rotatlOg pipe for analyzing dominant slOgularity behaviour of the flow, Two series rclated to respectively the perturbation parameter Re" (rotational Reynolds number) and similarity parameter K (=96/leflcfI, where ReI