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Adi-Kusumo, Fajar
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Social Sciences

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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.
Numerical Bifurcations and Sensitivity Analysis of an SIVPC Cervical Cancer Model Asih, Tri Sri Noor; Adi-Kusumo, Fajar; Wiraya, Ario; Forde, Jonathan
Communication in Biomathematical Sciences Vol. 7 No. 2 (2024)
Publisher : The Indonesian Bio-Mathematical Society

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/cbms.2024.7.2.8

Abstract

We consider a mathematical model of cervical cancer based on the Natural History of Cervical Cancer. The model is a five dimensional system of the first order of ordinary differential equations that represents the interaction between the free Human Papilloma Virus (HPV) population and four cells sub-populations, i.e., the normal cells, infected cells by HPV, precancerous cells, and cancer cells. We focus our analysis to determine the existence conditions of the nontrivial equilibrium point, the bifurcations, and the sensitivity of the parameters that play important roles in metastasis. Based on the basic reproduction ratio of the system, we found that the infection rate, the new viruses production rate, the free viruses death rate, the infected cells growth rate, and the precancerous cells progression rate play important roles for the cancer spreads in the cellular level. By applying sensitivity and numerical bifurcation analysis, we found that there are some important bifurcations that trigger some irregular behaviours of the system, i.e., fold, Hopf, cusp and Bogdanov-Takens.
Co-Authors Asih, Tri Sri Noor Forde, Jonathan Jannah, Nur Wahidiyatil Lina Aryati Wiraya, Ario