Viral dynamics are commonly modeled using systems of nonlinear ordinary differential equations to describe the interaction between target cells, infected cells, and free virus particles. The target cell–limited model has been extensively studied in the literature, where numerical solutions are typically obtained using fixed-step finite difference schemes such as the classical fourth-order Runge–Kutta (RK4) method. In this study, we solve the target cell–limited viral dynamics model using an embedded numerical scheme, namely the RKAHeM (4,4) method, which provides enhanced accuracy and error control. Numerical simulations are performed, and the obtained results show excellent agreement with previously reported solutions, thereby validating the effectiveness and robustness of the proposed method. GANITJ. Bangladesh Math. Soc.46.1(2026) 019–034
Efficient crop planning is very important in agriculture because farmers need to allocate limited resources such as land, labour, and budget while facing uncertainty in crop yield, demand, and prices. In this research, deterministic and stochastic programming models are developed to determine the optimal land allocation and crop production plan that maximizes farmers’ profit while meeting food scarcity. All parameters in the deterministic models are certain. To address the uncertain parameters, a 2-stage stochastic programming model is developed where the land allocation, demand, selling, and purchasing decisions are considered as uncertain. Primary data are collected from direct interviews with the farmers to validate the model. Secondary data collected from the Bangladesh Bureau of Statistics (BBS) Yearbook 2023 are also used. Uncertainty is analysed through a stochastic model with 4 scenarios. Both models are implemented and solved using the AMPL programming language. A comparative analysis indicates that although the deterministic model yields higher profit under fixed conditions, the stochastic model provides more robust and reliable decisions by incorporating uncertainty. Therefore, the proposed stochastic crop planning model can serve as an effective decision-support tool for farmers to manage agricultural risks and improve overall farm profitability. GANITJ. Bangladesh Math. Soc. 46.1 (2026) 01-18
We concentrate on the suppression of infectious diseases that give rise to temporary or imperfect immunity. It introduces a stochastic SVEIR model with vaccinated (V) and exposed (E) populations, and incorporates quarantine and isolation (i.e., social distancing) as the two principal control strategies. The model is defined on non-spatial networks and includes two parameters — the latent carrier rate (ρ) and the rate of conveying (μ) to characterise transmission behaviour in more realistic terms. This paper assesses the synergy between vaccination, isolation and quarantine policies, accounting for both voluntary and imposed behaviors as well as for the resource costs of interventions. The aim is to decide on the best vaccination strategy to achieve elimination. The strategy considers both proactive (e.g., vaccination) and reactive (e.g., isolation/quarantine) measures if we want to minimize the impact of pandemic. This joint control approach is based on a mean field theory based on the SVEIR model. GANIT J. Bangladesh Math. Soc. 45.2 (2025) 066–082
The quickest multi-commodity flow problem arises when more than one commodity is to be transported from the specific source nodes to corresponding sink nodes through the arcs in an underlying dynamic network within the minimum possible time. Sharing of the capacity of the bundle (common) arcs is one of the major issues for the multi-commodity flow problem. In this paper, we deal with the quickest multi-commodity flow problem by sharing the capacity of bundle arcs using proportional and flow-dependent capacity sharing techniques, which reduce the multi-commodity flow problem into single commodity flow problems. We present the polynomial and pseudo-polynomial algorithms to solve the problem by proportional and flow-dependent sharing, respectively. A three dimensional time-expanded layer graph is introduced to solve the problem with flow-dependent capacity sharing technique. GANIT J. Bangladesh Math. Soc. 45.2 (2025) 001–017
Diffuse Optical Tomography (DOT) is an emerging medical imaging technique. This method of imaging has incredible potential for global impact on access to healthcare due to low cost compared to other imaging modalities (X-Ray, CT, etc.). DOT is safer than the aforementioned modalities, and utilizes near-infrared light (NIRS), which is not harmful for humans. DOT is currently impractical because it produces scans that are not accurate enough for medical diagnoses. One point of inaccuracy is that NIRS is highly scattering while propagating through biomedical tissue (photons take a random variety of paths), so it is extremely difficult to find a model of this propagation that can support accurate image reconstruction. This project compares the Monte Carlo Model and Diffusion Equation Model of photon transport. The Monte Carlo Model (MCM) is well known to be extremely accurate, however is too computationally intensive to put into practice. The Diffusion Equation Model is a partial differential equation approximation of the MCM, so it is less accurate, however more efficient. By using the ValoMC software to simulate the MCM and the Toast++ software to simulate the Diffusion Equation Model, both with a variety of parameters, a pattern of approximation error in solutions of photon fluence can be found and modeled. The main objective is to use these models of approximation error to transform Toast++’s raw solutions to be more similar to the ValoMC solutions, and therefore more accurate. GANIT J. Bangladesh Math. Soc. 45.2 (2025) 045–053
In this paper, we discuss fractional differential equations, including the Fokker-Planck equation and fractional diffusion differential equations, which are closely related to chemistry and engineering. To solve these equations, we employ the Laplace Variational Iteration Method (LVIM), which combines the Laplace transform with He’s Variational Iteration Method. To demonstrate the efficiency and validity of LVIM, we consider two 1-D Fokker-Planck equations and three fractional diffusion equations in 1-D, 2-D, and 3-D. We solve these equations using LVIM, and the results are presented analytically in tables and graphically using MATLAB for different values of the fractional order and these results are then compared with those obtained by existing methods. The solutions obtain as infinite series, and for certain values of the fractional order, they are found to be similar to the exact results. GANIT J. Bangladesh Math. Soc. 45.2 (2025) 031–044
The primary goal of this article is to expose the four concepts of fuzzy soft spaces that underlie the comprehension of fuzzy topological spaces. We then go into some new theories and the implications of such spaces. Additionally, authors like speculating on the relationships between these ideas and offering fresh perspectives on certain traits. GANIT J. Bangladesh Math. Soc. 45.2 (2025) 054–065
In this paper, we develop a unified mathematical framework for nonlinear diffusion in the human respiratory system, coupling gas exchange with fluid dynamics in both healthy and diseased lungs. We generalize Fick’s second law by making diffusivity concentration-dependent D(C) = D0(1 + αC), modeling effects such as inflammation or tissue damage. Three finite difference schemes (explicit, implicit, Crank-Nicolson) are used to solve the nonlinear PDE, with the Crank-Nicolson method being most accurate (second-order convergence) and stable. Analytical solutions to the linear problem confirm the numerical methodology. Through a traveling wave transformation C(x, t) = U(z), z = x − vt, the PDE is reduced to an ODE system, allowing phase-plane analysis of wave propagation and steady states. Theoretical and computational results are bridged by this framework, which provides a flexible tool to investigate oxygen transport and fluid buildup in diseases such as emphysema or pleural effusion. Predicting spatial-temporal disease progression, the results demonstrate its potential, with applications in clinical modeling and therapeutic studies. GANIT J. Bangladesh Math. Soc. 45.2 (2025) 018–030
The study investigates the intricate interactions, particularly the antagonistic dynamics, between two entities inhabiting a nonhomogeneous circumstance subjected to harvesting pressures. We initiate our analysis by constructing a robust mathematical framework utilizing partial differential equations (PDEs) to model the behaviors of the two species. We rigorously demonstrate the substantiality and exclusivity of solutions to the formulated model. In this context, we establish pivotal conditions that facilitate species coexistence, as well as delineate scenarios wherein one species may exert competitive pressures sufficient to drive the other towards extinction. Additionally, we identify conditions that could culminate in the simultaneous extinction of both species. The findings yield a comprehensive relative analysis of two distinct harvesting levels, providing critical insights into their differential impacts on species dynamics. Furthermore, we substantiate our theoretical conclusions through a series of numerical simulations, which serve to validate our model and its implications. J. Bangladesh Math. Soc. 45.1 (2025) 32–49
Computer-Aided Geometric Design (CAGD) is a branch of applied mathematics that focuses on the computational modeling and representation of geometric shapes. It plays a crucial role in diverse fields such as geographic information systems, computer gaming, medical imaging, robotics, engineering, and traditional industries like automobile, aircraft, and ship design. A core challenge in CAGD is the creation of smooth curves and surfaces through efficient mathematical techniques. In recent years, subdivision schemes have emerged as a practical and elegant method for generating smooth limit curves. These techniques are widely used in computer animation (CA), CAGD, and computer graphics (CG) due to their simplicity, flexibility, and effectiveness. This study presents three prominent subdivision schemes which as the Chaikin Subdivision (CS), Corner-Cutting Subdivision (CSS), and Four-Point Subdivision (FPS) schemes. Each operates by refining an initial control polygon through iterative rules that add new points as weighted combinations of existing ones. Repeated application of these rules produces a limit curve with increasing smoothness. We begin by constructing various initial shapes—such as a jar, a mango, pi, and a car—and applying the CS scheme at multiple subdivision levels. Next, we apply the CSS scheme to shapes like a rabbit, a five-fingered hand, and a pi. Finally, the FPS scheme is applied to “U”, mug, and pi shapes. The results convincingly demonstrate the capability of these schemes to produce smooth and visually appealing curves with high precision. Looking ahead, our future research aims to develop and investigate non-uniform variants of these schemes. This direction seeks to improve adaptability for handling complex and irregular geometries, while maintaining the core properties of convergence, smoothness, and visual fidelity—ultimately expanding their utility in advanced geometric modeling. J. Bangladesh Math. Soc. 45.1 (2025) 50–63
The transmission dynamics of the dengue disease with imperfect vaccination and re-infection are being considered & analyzed. The model exhibits backward bifurcation when the basic reproduction number (R0) is less than 1. However, using the Lyapunov function as well as the LaSalle Invariance Principle, it is demonstrated that with perfect vaccination and no re-infection, the DFE point is globally asymptotically stable. If R0 > 1, there exists a distinct endemic equilibrium that is locally asymptotically stable. Numerical results of the model, using relevant parameter values, indicate that the increasing rate of vaccination waning resulted in the increase of infected individuals. Further numerical results suggest that the disease will continue in the community in the presence of re-infection. It also suggests that the dengue virus can be controlled effectively using the perfect vaccine. J. Bangladesh Math. Soc. 45.1 (2025) 16–31
This study extends the classical Susceptible-Infected-Recovered (SIR) model by integrating adaptive behaviors and policy interventions during epidemics through the Signal-SIR model. Here the susceptible population is divided into two groups: individuals who adhere to health regulations (AD strategy) and those who do not (NAD strategy). The model simulates the dynamic interaction between government signals and public behavior where it utilizes replicator dynamics to explore how health warnings influence population responses. It also introduces chicken game payoffs to analyze the redistribution of risks between compliant and non-compliant individuals. To optimize model parameters and explain time-varying dynamics, deep neural networks (DNNs) has been employed alongside Stochastic Gradient Descent. We establish a loss function that quantifies the discrepancies between observed data and model predictions. Simulation results indicate that enhanced adaptive behavior, driven by enhanced adherence to health regulations, significantly reduces the spread of infection. Therefore, it leads to lower infection peaks and higher recovery rates. This paper highlights the critical role of adaptive strategies in public health policy and provides a data-driven framework for effectively forecasting and managing epidemic dynamics. J. Bangladesh Math. Soc. 45.1 (2025) 01–15
Mantle convection, a fundamental mechanism controlling the dynamics of the Earth’s surface and interior, shows different behaviors caused by different factors such as viscosity variation, viscous dissipation, internal heating, and so on. In this paper, the effects of temperature-dependent viscosity, temperature and pressure-dependent viscosity and viscous dissipation on mantle convection are investigated in elongated and narrow cells. The Rayleigh-B´enard convection model is solved numerically with the full form of the Arrhenius viscosity function at a high Rayleigh number for viscosity contrasts up to 1030. The root mean square velocity and Nusselt number are computed and tabulated. The thermal characteristics and flow dynamics inside the convection cell are presented by temperature profiles and stream function contours. These simulated results indicate that increasing viscosity contrasts with the incorporation of viscous dissipation weakens the convection vigour and heat transfer in the mantle. The selected narrow cell remains stable for a very high viscosity contrast at different viscous pressure number μ, whereas the selected elongated cell with temperature-dependent viscosity and strong viscous dissipation becomes unstable and single-cell pattern breaks down at high viscosity variation. J. Bangladesh Math. Soc. 44.2 (2024) 077–096
In this study, we explore the effectiveness of the Finite Element Method (FEM) employing linear shape functions to address problems governed by Dirichlet, Neumann, and Robin boundary conditions. We use the derived weak formulation of FEM to solve various types of partial differential equations (PDEs) with mixed boundary conditions. Convergence and stability analyses are carried out to evaluate the performance of this approach, and different types of errors, like absolute error, dissipation, dispersion, and total mean square error, are investigated. This method is applied, and both the exact and approximate solutions are tabulated in three distinct cases: a one-dimensional Burgers-Huxley equation with Dirichlet boundary conditions; a diffusionreaction equation with Neumann boundary conditions; and a uniformly propagating shock problem with Robin boundary conditions. Approximate solutions are compared to exact ones through 2D and 3D graphical representations, and tabular data offers a thorough error analysis. Additionally, error maps provide strong evidence for the accuracy of the suggested approach, demonstrating its capacity to precisely and quickly solve challenging problems with a variety of boundary conditions. J. Bangladesh Math. Soc. 44.2 (2024) 047–064
There are numerous currency models, but only a few are suitable for practical use. The Liu-Chen-Ralescu (L-C-R) model, proposed by Liu, Chen, and Ralescu, is one of them, where the exchange rate abides by an uncertain differential equation. However, the model treats interest rates as constants, which is unrealistic given the fluctuations in financial markets caused by various human-caused or natural disasters. Our preliminary intention was to explore a model that incorporates additional parameters such as log drift, log diffusion, and variance of the observed data. We discovered a new currency model, referred to as the X-W model, which was proposed by Xiao Wang in his 2019 research article. He proposed that an uncertain differential equation governs the exchange rate, while stochastic differential equations govern both domestic and foreign interest rates. Since the X-W model considers various circumstances and calculates more parameters, the option prices are assumed to be higher. We find the call and put currency option prices for the X-W model using Euler’s method and trapezoidal rule in this article and then the option prices have been compared with the currency option prices obtained from the L-C-R model. Finally, we present some numerical and graphical results for both models using MATLAB coding for better observation. We were successful in finding our expected results and can finally conclude that the X-W model is a better fit for the real market. J. Bangladesh Math. Soc. 44.2 (2024) 065–076
At the time of evacuation, placement of the facilities for the support of evacuees is an important task. The proper allocation of the facilities in such a way that the reduction in the flow value due to the placement of facilities on the arcs is minimal, is another important aspect of the problem. In this paper, we introduce an evacuation planning problem with facility allocation by using bi-level formulation. The upper level problem identifies the best possible location and lower level problem finds the optimal solution in the network with facility allocation. We solve the problem with a naive approach of combinatorial optimization and the Karush-Kuhn-Tucker (KKT) transformation. J. Bangladesh Math. Soc. 44.2 (2024) 017–027
Cryptography is the technique to protect sensitive information from unauthorized persons by encryption. Cryptographers have invented various systems of cryptography to make it befitting. In the age of modern science, the use of mathematical theories has added a new dimension to cryptography. Prime factorization-based cryptography is widely used and effective. In 1977, Rivest, Shamir, and Adlerman proposed the first practical public key cryptosystem based on the prime factorization of large numbers known as the RSA cryptosystem. Later in 1979, Michael Oser Rabin developed a technique based on prime-factorization known as Rabin Cryptosystem. Several variants of these systems have been developed further by many famous mathematicians and computer scientists, aiming to increase security, reduce cost, time, and memory usage, and enhance overall performance. Tsuyoshi Takagi and Hugh C. Williams proposed such two famous variants. In this paper, we have first analyzed the traditional cryptosystems and existing variants. Identifying the security strength and field of improvement of these systems and their variants, we have proposed two new variants. The encryption-decryption techniques are described by employing them in several applications. The effectiveness of the proposed variants is demonstrated by a comparative analysis of these variants with others. Numerical experiments show that the proposed Rabin’s variant performs almost the same as the base algorithm. However, the proposed variant of RSA algorithm reduces computational time significantly, approximately 91% reduction from traditional RSA and 90% reduction from multi-prime RSA. J. Bangladesh Math. Soc. 44.2 (2024) 01–16
In this paper we introduce the class of Rationalized Toeplitz Hankel operators on the space L2(Tn), T being the unit circle in complex plane and L2(Tn) is the space of Lebesgue square integrable functions on Tn. We also introduce the Rationalized Toeplitz Hankel matrix of level n and give the characterization of Rationalized Toeplitz Hankel Operator. J. Bangladesh Math. Soc. 44.2 (2024) 039–046
Complex fuzzy set (CFS) is an extension of the fuzzy set (FS) which can deal with ambiguity by allowing a complex-valued membership degree of an element of a universal set. A host of researchers studied the complex fuzzy sets in theoretical and practical due to their amplitude term and phase term membership degrees. At present, various applications of fuzzy correlation and correlation coefficients have emerged by numerous researchers. But most of the works are related to real fuzzy data. In this article, we introduce the concept of the correlation coefficient of the complex fuzzy sets and some of its related properties are described. Furthermore, an application of the correlation coefficient of the complex fuzzy sets in pattern recognition is illustrated. To show the reliability and validity of our technique, we explain a comparative study with the existing method. J. Bangladesh Math. Soc. 44.2 (2024) 028–038
Machine Learning techniques have gained prominence in medical diagnosis due to their ability to uncover patterns in complex data-sets, thereby giving accurate disease classification. In this study, we mainly focus on the application of two widely used Machine Learning algorithms, Logistic Regression and K-Nearestneighbors( KNN), for the purpose of distinguishing patients with diabetes from those without. Our research aims to shed light on the comparative accuracy and performance of these algorithms in a medical context. The methodology section outlines experimental setup, detailing data processing, algorithm training and testing procedures. A comprehensive data-set comprising medical attributes is utilized for evaluation and accuracy metrics are employed to quantify the performance of the algorithms. Results has shown efficacy of both the algorithms and our findings showcase the strengths and limitations of each approach, contributing on the applicability in medical decision making. By offering a nuanced comparison, we illuminate a path for more robust and accurate disease identification techniques, further enhancing patient care and medical outcomes. GANIT J. Bangladesh Math. Soc. 43.1 (2023) 01- 07
