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All Journal Communication in Biomathematical Sciences Jambura Journal of Biomathematics (JJBM)
Kalyan Das
Sambalpur University Institute of Information Technology
Computer Science & IT Decision Sciences, Operations Research & Management Mathematics Social Sciences

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Impact of Nanomaterial in the Marine Environment: Through Mathematical Modelling by Eco-Path Framework Das, Kalyan; Srinivas, M.N.; Saikh, Aktar; Biswas, Md. Haider Ali
Communication in Biomathematical Sciences Vol. 7 No. 1 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.1.8

Abstract

We propose and analyze a simple modification to the Rosenzweig-MacArthur predator (zooplankton)-prey (phytoplankton) model to account for the interference of the predators with the impacts of nanoparticles. We have taken into account the influence of predators by quantifying the impact of nanoparticles in actual environments. It is shown that the influence of the nanoparticles may reduce the prey's maximum physiological per-capita growth rate. An elementary Lotka-Volterra uptake term is taken into consideration in order to investigate the nanoparticle dynamics or interactions. Most importantly, our research shows that phytoplankton growth suppression caused by nanoparticles can destabilize the system and cause periodic oscillation. Additionally, it was demonstrated that a decrease in the equilibrium densities of both phytoplankton and zooplankton might occur from an increase in the rate of interaction between the nanoparticles and phytoplankton. Additionally, the study shows that the stable coexistence of the system dynamics depends critically on the aquatic system's nanoparticles being depleted. We also looked into the system using different kinds of functional reactions. Compared to other commonly used ecology, The complex relationship that exists between phytoplankton and nanoparticles in the natural environment is better described by the Monod-Haldane functional response.
Bifurcation analysis of phytoplankton-fish model through parametric control by fish mortality rate and food transfer efficiency Das, Kalyan; Madhusudanan, V.; Srinivas, M. N.; Kabir, Md Humayun; Gani, Md Osman; Islam, Sardar M. N.
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 2: December 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v4i2.21480

Abstract

An Algae-zooplankton fish model is studied in this article. First the proposed model is evaluated for positive invariance and boundedness. Then,the Routh-Hurwitz parameters and the Lyapunov function are used to determine the presence of a positive interior steady state and the criteria for plankton model stability (both local and global). Taylor's sequence is also used to discuss Hopf bifurcation and the stability of bifurcated periodic solutions. The model's bifurcation analysis reveals that Hopf-bifurcation can occur when mortality rate and food transfer efficiency are used as bifurcation parameters. Finally, we use numerical simulation to validate the analytical results.
A Qualitative Analysis of Leukemia Fractional Order SICW Model Das, Kalyan; Kumar, G. Ranjith; Ramesh, K.; Biswas, Md. Haider Ali
Jambura Journal of Biomathematics (JJBM) Volume 5, Issue 1: June 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v5i1.24961

Abstract

Using a series of fundamental differential equations, including the Caputo derivative, which makes it easier to specify the initial conditions of the differential equations, we present a fractional order concept of leukemia in this study. The universality, positivity, and boundedness of solutions are first established. The local stability properties of the equilibrium are studied using the fractional Routh-Hurwitz stability criteria. The differential equation system has been solved using unconventional finite difference techniques. The Leukemia Fractional Order SICW model introduces several innovative elements compared to traditional epidemiological and disease models. This stands out due to its integration of fractional-order differential equations, inclusion of leukemic cells and immune cells compartments, simulation of treatment strategies, consideration of waning immunity, and its application to leukemia-specific scenarios. These elements collectively make it a valuable tool for studying leukemia dynamics, exploring treatment options, and improving our understanding of how the immune system interacts with cancer cells in leukemia patients. Numerical simulations of the model are shown at the conclusion to interpret our theoretical outcomes in support of various fractional orders of derivative   options. From there, we can observe how the evolution of the system components is impacted by the fractional derivative .
Co-Authors Biswas, Md. Haider Ali Gani, Md Osman Islam, Sardar M. N. Kabir, Md Humayun Kumar, G. Ranjith Madhusudanan, V. Ramesh, K. Saikh, Aktar Srinivas, M. N. Srinivas, M.N.