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All Journal Epsilon: Jurnal Matematika Murni dan Terapan Communication in Biomathematical Sciences
Jannah, Nur Wahidiyatil
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Decision Sciences, Operations Research & Management Social Sciences Transportation

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A Mathematical Model of Social Interaction between the Sufferers of Cardiovascular and Type 2 Diabetes Mellitus Jannah, Nur Wahidiyatil; Aryati, Lina; Adi-Kusumo, Fajar
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.2024.7.1.5

Abstract

Type 2 diabetes mellitus is a non-communicable medical condition that is most commonly suffered in compare to type 1 diabetes, gestational diabetes, or diabetes that is caused by pathogen or disorders. The other important non-communicable medical condition is cardiovascular disease that occurs due to impaired blood circulation in the heart and blood vessels. The unhealthy lifestyle behaviors that mainly influenced by social interactions play an important role to increase the number of prevalence for those diseases. In this paper, we consider a mathematical model of the social interactions effects to the sufferers of the cardiovascular and type 2 diabetes mellitus diseases. We separate the population to five sub populations, i.e., individuals with normal weight, individuals who have obesity, individuals with cardiovascular disease only, individuals with type 2 diabetes mellitus disease only, and individuals with both cardiovascular and type 2 diabetes mellitus diseases. By using linear analysis and bifurcation theory, we determine the steady state conditions analytically and show some scenarios for the population based on variation of the parameters value numerically.
NON-STANDARD SCHEME DISCRETIZATION (NSFD) FOR COMMENSALISM SYMBIOSIS MODEL WITH HARVESTING IN COMMENSAL POPULATIONS Puspitasari, Nurmaini; Faisal, Faisal; Yulida, Yuni; Jannah, Nur Wahidiyatil; Balya, Muhammad Afief
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.16551

Abstract

Dynamic analysis on the model of commensalism symbiosis with the discretized Michaelis-Menten cropping by using different schemes to non-standard finite difference (NSFD) is the main focus in this article. The analysis is started by searching the equilibrium points with their existence terms and local stability with their stability terms. In this article, there are four equilibrium points. The points are the extinction point of both populations, the host extinction point, the commensal extinction point, and the point where both populations can coexist (the coexistence equilibrium point). The existence of a host extinction point and a point at which both populations can coexist depends on the conditions of existence that must be met. Among the four equilibrium points, the commensal extinction point and the coexistence equilibrium point are locally asymptotically stable provided that the specified stability conditions are met. In the final analysis, numerical simulations were performed using the 4th order Runge–Kutta scheme for the continuous model and the NSFD scheme for the discrete model. The results show that the NSFD scheme offers greater flexibility in choosing the integration time step to ensure convergence to a feasible solution, outperforming the 4th order Runge–Kutta scheme in this respect.
Co-Authors Adi-Kusumo, Fajar Balya, Muhammad Afief Faisal Faisal Lina Aryati Puspitasari, Nurmaini Yuni Yulida