https://repository.auw.edu.bd/handle/123456789/63 2026-05-06T11:50:59Z 2026-05-06T11:50:59Z Kamrujjaman, Md. https://repository.auw.edu.bd/handle/123456789/3376 2026-03-05T10:45:32Z 2025-03-26T00:00:00Z

Assessing the Trade-Off between Voluntary and Forced Interventions to Control the Emergence of Recurring Pandemics—An Evolutionary Game-Theoretic Modeling Kamrujjaman, Md. In this study, we aim to examine the dynamics of diseases by employing both voluntary and forced control strategies backed by evolutionary game theory (EGT). The impact of quarantine is investigated through our suggested frame- work provided that a partial adoption of voluntary vaccination is observed at the earlier stage. The combined and individual effect of dual preventive pro- visions are visualized through SEIR-type epidemic model. Additionally, the effect of coercive control policies’ efficacy on individual vaccination decision is illustrated through the lens of EGT. We also consider the cost associated with vaccination and quarantine. The numerical simulations shown in our work emphasize how important it is to put quarantine rules in place to stop the spread of infection. These restrictions imposed by the government can be relieving, especially during times when a sizable section of the populace is re- luctant to get vaccinated because of its ineffectiveness or excessive cost. We also show when and under what circumstances one policy works better than the other. How these policies’ compliance rates should be calculated is there- fore becomes a focal point of discussion. We support this claim by producing phase diagrams for three different evolutionary outcomes throughout our in- vestigation and changing the two crucially important pick-up rate parameters, one connected with the quarantine policy and the other is related to the isola- tion policy, in various directions. We then additionally examine the efficacy and cost associated with different policy adaption. This model effectively high- lights the importance of dual provisional safety in understanding public health issues by using the mean-field approximation technique, which aligns with the well-known imitation protocol known as individual-based risk assessment dynamics.

2025-03-26T00:00:00Z Kamrujjaman, Md. https://repository.auw.edu.bd/handle/123456789/3375 2026-03-05T10:45:35Z 2025-01-01T00:00:00Z

Mathematical Analysis of a Resource-Based Dispersal Model With Gompertz Growth and Optimal Harvesting Kamrujjaman, Md. Gompertz dynamics offer significant applications for the growth of invasive species, cancer modeling, optimal harvesting policies, sustainable yield, and maintaining population levels due to its pattern formation in low-density cases. This paper examines a widely applicable nonhomogeneous diffusive Gompertz law with zero Neumann boundary conditions, where all coefficients are smooth periodic functions. The analytical approach explains the ubiquitous stability of a time-periodic solution and seeks the optimal strategy for harvesting under the Gompertz growth law, potentially generalizing the results for many small organisms, including plants and wild populations. The proposed model successfully investigates the dynamics with and without diffusion. Moreover, the spatio-temporal equation more precisely describes the population’s evolutionary processes using a generalized classical reaction-diffusion equation. Finally, we observe several potential applications, outlining the optimal strategies for real-world scenarios and related fields where optimal harvesting is utilized.

2025-01-01T00:00:00Z Kamrujjaman, Md. https://repository.auw.edu.bd/handle/123456789/3374 2026-03-05T10:45:30Z 2025-10-25T00:00:00Z

Solutions of Nonlinear Parabolic PDEs: A Novel Technique Based on Galerkin-Finite Difference Residual Corrections Kamrujjaman, Md. Numerical solutions for second-order parabolic partial differential equations (PDEs), specifically the nonlinear heat equation, are investigated with a focus on analyzing residual corrections. Initially, the Galerkin weighted residual method is employed to rigorously formulate the heat equation and derive numerical solutions using third-degree Bernstein polynomials as basis functions. Subsequently, a proposed residual correction scheme is applied, utilizing the finite difference method to solve the error equations while adhering to the associated error boundary and initial conditions. Enhanced approximations are achieved by incorporating the computed error values derived from the error equations into the original weighted residual results. The stability and convergence of the residual correction scheme are also analyzed. Numerical results and absolute errors are compared against exact solutions and published literature for various time and space step sizes, demonstrating the effectiveness and precision of the proposed scheme in achieving high accuracy.

2025-10-25T00:00:00Z Kamrujjaman, Md. https://repository.auw.edu.bd/handle/123456789/3373 2026-03-05T10:45:33Z 2025-09-01T00:00:00Z

Effectiveness of bed nets and media awareness in dengue control: A fuzzy analysis Kamrujjaman, Md. The incorporation of fuzzy analysis in the mathematical modeling of disease outbreaks has brought a paradigm shift in epidemiological research, offering a sophisticated approach to understanding and addressing the complexities inherent in disease dynamics. Unlike traditional mathematical models, which often rely on deterministic assumptions and precise parameter values, fuzzy analysis provides a flexible framework capable of accommodating uncertainty and imprecision within epidemiological systems. This paper presents a novel SVEIR-SEI com- partmental model for dengue disease where five key parameters such as transmission rate, mortality rate, recovery rate, biting rate, and vaccination rate are treated as fuzzy numbers. Among these, transmission rate, mortality rate, and recovery rate are defined as a function of virus load whereas biting rate and vaccinations rate are defined as a function of number of bed net users and media awareness regarding vaccination, respectively. Crisp reproduction number is determined using next generation matrix method and hence fuzzy reproduction number is derived as a triangular fuzzy number (TFN). Numerical results show that biting rate and vaccination rate are the two most sensitive parameters to crisp reproduction number. We also examine the impact of using bed nets and media awareness regarding vaccination on the model system under fuzzy environment. It is found that using bed nets is a more effective strategy for dengue control than media coverage regarding vaccination.

2025-09-01T00:00:00Z