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##### Nazrul Islam

Work place: Department of Mathematics, Jashore University of Science and Technology, Jashore – 7408, Bangladesh

E-mail: nazrul.math@just.edu.bd

Website:

Research Interests: Mathematics

Biography

Nazrul Islam completed his B.Sc. (Honor’s)) in Mathematics from the University of Dhaka. He obtained his M.Sc. (Master’s) in Applied Mathematics from the same university. He is currently working as a lecturer in the Department of Mathematics, Jashore University of Science and Technology, Jashore-7408, Bangladesh. His research interests are applied mathematics, numerical solution of ODE, PDE and spline approximations.

##### Application of Mathematical Modeling: A Mathematical Model for Dengue Disease in Bangladesh

DOI: https://doi.org/10.5815/ijmsc.2024.01.03, Pub. Date: 8 Feb. 2024

A virus spread by mosquitoes called dengue fever affects millions of people each year and is a serious threat to world health. More than 140 nations are affected by the illness of dengue fever. Therefore, in this paper, a Susceptible-Infectious-Recovered (SIR) mathematical model for the host (human) and vector (dengue mosquitoes) has been presented to describe the transmission of dengue in Bangladesh. In the model the vector are related with two compartments that are susceptible and infective and host are related with three compartments that are susceptible, infective, and recovered. By these five compartments, five connected nonlinear ordinary differential equations (ODEs) are produced. As a result of non dimensionalization, a system of three nonlinear ODEs has been generated. The reproductive number and equilibrium points have been estimated for different cases. In order to compute the infection rate, data for infected human populations have been gathered from multiple health institutes in Bangladesh. MATLAB has been utilized to construct numerical simulations of different compartments in order to examine the impact of critical parameters on the disease’s propagation and to bolster the analytical findings. The simulated outcomes for susceptible, infected, and eliminated in graphical formats have been displayed. The paper’s main goal is to emphasize the uniqueness of computational analysis of the SIR mathematical model for the dengue fever.

##### Determination of Optimal Smoothing Constants for Foreign Remittances in Bangladesh

DOI: https://doi.org/10.5815/ijmsc.2021.04.02, Pub. Date: 8 Dec. 2021

Remittance is the tie that is sent to the country by earning money from abroad. In present Bangladesh, remittance is playing an important role in increasing reserves and revenue. For about two decades remittance has been contributing a huge portion of export earnings. Remittances have a significant impact on the budget of Bangladesh and also the budget depends a lot on remittances. So it is very crucial to know the future remittance to make an annual budget for upcoming year. This paper concentrates on choosing the appropriate smoothing constants for foreign remittances forecasting by Holt’s method. This method is very popular quantitative skilled in forecasting. The forecasting of this deftness depends on optimal smoothing constants. So, choosing an optimal smoothing constant is very important to minimize the error of forecasting. We have demonstrated the techniques by presenting actual remittances and also presented graphical comparisons between actual and forecasting remittances for the optimal smoothing constants.

##### Accuracy Analysis for the Solution of Initial Value Problem of ODEs Using Modified Euler Method

DOI: https://doi.org/10.5815/ijmsc.2021.02.04, Pub. Date: 8 Jun. 2021

There exist numerous numerical methods for solving the initial value problems of ordinary differential equations. The accuracy level and computational time are not the same for all of these methods. In this article, the Modified Euler method has been discussed for solving and finding the accurate solution of Ordinary Differential Equations using different step sizes. Approximate Results obtained by different step sizes are shown using the result analysis table. Some problems are solved by the proposed method then approximated results are shown graphically compare to the exact solution for a better understanding of the accuracy level of this method. Errors are estimated for each step and are represented graphically using Matlab Programming Language and MS Excel, which reveals that so much small step size gives better accuracy with less computational error. It is observed that this method is suitable for obtaining the accurate solution of ODEs when the taken step sizes are too much small.