Post graduate dissertations (Theses) of Mathematics (Math) http://lib.buet.ac.bd;localhosthttp://:8080/xmlui/handle/123456789/638 2026-04-14T14:44:14Z 2026-04-14T14:44:14Z Ali Ahmad http://lib.buet.ac.bd;localhosthttp://:8080/xmlui/handle/123456789/7225 2025-12-09T07:06:57Z 2024-10-06T00:00:00Z

Bifurcation analysis of multi-control strategy- an epidemiological approach Manirul Alam Sarker, Dr. Md.; Ali Ahmad; 0421092510; 517.38/ALI/2025 For a long time, serious public health concerns have been related to the COVID-19 outbreak caused by SARS-CoV-2. Mathematical models are useful in examining the dynamics of the disease transmission, prediction and control when a suitable drug or vaccine is unavailable. In this study, vaccination and quarantine strategies with mask efficiency, a susceptible, vaccinated, exposed, infected, quarantined and recovered (SVEIQR) compartmental model for COVID-19 is presented. Qualitative properties for the proposed model, such as positivity and boundedness of solutions, existence and uniqueness of solutions and analysis of equilibria will be performed. The control reproduction number is calculated using the next-generation matrix method. Local stability for both disease-free equilibrium (DFE) and disease-endemic equilibrium (DEE) will be tested. With Lyapunov's direct method, the global stability of the model is established. Explicit conditions are obtained to classify different bifurcations, including saddle-node bifurcation, transcritical bifurcation, pitch-fork bifurcation, forward and backward bifurcation. The forward bifurcation phenomenon in the model is demonstrated when the control reproduction number is greater than one. It is also noticed that under the perfect vaccine efficacy, the model exhibits the transcritical bifurcation phenomenon. However, the proposed model will not exhibit the saddle-node and pitch-fork bifurcation. Furthermore, it is found that an effective vaccination strategy with proper face mask usage is highly necessary to reduce the burden of diseases instead of a quarantine strategy.

2024-10-06T00:00:00Z Fahimur Rahman Shuvo, Md. http://lib.buet.ac.bd;localhosthttp://:8080/xmlui/handle/123456789/7215 2025-12-08T04:32:00Z 2024-06-01T00:00:00Z

Exploring the eco-evolutionary dynamics of cyclic dominance in rock-paper-scissors strategies within pairwise dilemma games Ariful Kabir, Dr. K M; Fahimur Rahman Shuvo, Md.; 0422093001; 519.3/FAH/2024 Cooperation, selfishness, and dilemma are prevalent in diverse contexts, spanning from biological systems to human societies. Gaining insight into the mechanisms that facilitate and sustain cooperation is essential for effectively tackling global challenges such as climate change, resource depletion, and epidemics. This study presents a new ecological-evolutionary game theory model called the Pairwise Loner Game (PLG). The model combines the Optional Prisoner's Dilemma (OPD) and Rock-Paper-Scissors (RPS) games by incorporating an environmental feedback variable. The study alters the payoff matrices of the OPD and RPS games to guarantee compatibility and generates a comprehensive PLG payoff matrix that includes the environmental state. The replicator dynamics that govern the changes in strategy frequencies and the differential equation that describes the dynamics of the environment are established. Numerical simulations and analyses demonstrate that the environmental influence function is pivotal in determining environmental tipping points. This function models how the environment responds to the frequencies of different strategies, which in turn affects the availability of resources and the overall stability of the system. The simulations reveal that minor changes in the environmental influence function can lead to significant shifts in tipping points, highlighting the sensitivity of the system to environmental feedback. Additionally, the presence of all three strategies—cooperators, defectors, and loners—is significant for promoting a stable and sustainable environment. Cooperators contribute to resource replenishment, defectors exploit resources, and loners abstain from interaction, creating a dynamic balance that prevents the dominance of any single strategy and supports the long-term sustainability of the environment. This intricate interplay underscores the importance of maintaining diversity in strategies to enhance the resilience of ecosystems and social systems against external shocks and internal fluctuations.

2024-06-01T00:00:00Z Abdul Hye, Md. http://lib.buet.ac.bd;localhosthttp://:8080/xmlui/handle/123456789/7214 2025-12-08T04:14:42Z 2025-01-19T00:00:00Z

Dynamic optimization technique to reduce the health complexity of covid-19 Co-infection with severe diseases Forhad Uddin, Dr. Mohammed; Abdul Hye, Md.; 1018094001; 517.62/ABD/2025 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.

2025-01-19T00:00:00Z Nurain Arju http://lib.buet.ac.bd;localhosthttp://:8080/xmlui/handle/123456789/7207 2025-12-06T06:31:38Z 2024-02-17T00:00:00Z

Predicting age-specific female population of Bangladesh in 2026 using the leslie matrix model Farid Uddin Ahmed, Dr. Khandker; Nurain Arju; 0421092507; 512.896/NUR/2024 Bangladesh is one of the most densely populated countries in the world. According to the preliminary census report of Bangladesh Census and Household Census 2022, at the period of the census in 2022 population of Bangladesh in total is 16,51,58,616. Among them, the total number of females and males is 8,33,47,206 and 8,17,12,824, respectively. As a country’s equilibrium in environment, economics, and even administration is highly influenced by its population, these demographic data are essential for a well-regulated impact. Population projection aids in obtaining a country’s desired population for its overall prosperity. A widely used model to project the population is the Leslie matrix model. In this work, by using female survival and birth rates, the Leslie matrix model is applied to predict the age-specific female population and population growth of Bangladesh in 2026. The eigenvalues of the Leslie matrix are used to calculate the female population growth rate, where the principal eigenvalue is taken as the desired growth rate and the eigenvector is used to obtain the number of age-specific female populations. According to this research, the female population of Bangladesh will increase with a growth rate of 1.22 (approximately).

2024-02-17T00:00:00Z