APPLICATION OF DETERMINISTIC MODEL FOR HYPERTENSION CASES
Abstract
World Health Organization (WHO) latest reports about hypertension as a global health problem, due to a spike in cases. One of the roles of mathematics in health is to provide information about the increase in hypertension sufferers. Using a deterministic model is supposed to provide information that can explain how the cases increase. The deterministic model used is divided into two equations. The first equation uses k as a constant. Second, is p for p < 1 and p > 1. The results from both equations are in the form of a logistic curve and show simulation results are similar to condition data for hypertension sufferers. In addition, the extended deterministic model with p <1 indicates that hypertension sufferers increase exponentially, thus an intervention step is needed.
Downloads
References
P. Nugroho, H. Andrew, K. Kohar, C. A. Noor, and A. L. Sutranto, “Comparison between the world health organization (WHO) and international society of hypertension (ISH) guidelines for hypertension,” Ann. Med., vol. 54, no. 1, pp. 837–845, Dec. 2022, doi: 10.1080/07853890.2022.2044510.
World Health Organization (WHO), Global Report on Hypertension: The Race Against a Silent Killer. Genewa: World Health Organization, 2023.
K. K. R. I. (Kemenskes), Hasil Utama RISKESDAS. Indonesia, 2018.
T. Adiwati and N. Chamidah, “Modelling of hypertension risk factors using penalized spline to prevent hypertension in Indonesia,” IOP Conf. Ser. Mater. Sci. Eng., vol. 546, no. 5, p. 052003, Jun. 2019, doi: 10.1088/1757-899X/546/5/052003.
P. Andriani and N. Chamidah, “Modelling of Hypertension Risk Factors Using Logistic Regression to Prevent Hypertension in Indonesia,” J. Phys. Conf. Ser., vol. 1306, no. 1, p. 012027, Aug. 2019, doi: 10.1088/1742-6596/1306/1/012027.
M. N. Dalengkade, M. Yusniar, W. Tjape, F. I. Boleu, and O. Buka, “Penerapan polinomial orde-n dan Malthusian pada studi kasus kajian daya tampung wisatawan,” JST Jurnal Sains dan Teknol., vol. 10, no. 2, pp. 220–229, Nov. 2021, doi: 10.23887/jstundiksha.v10i2.38969.
M. Kaseside, F. Imanuel Boleu, R. Simanjuntak, B. Raymond Toisuta, and M. Nikolaus Dalengkade, “Penerapan model Malthusian, studi kasus: ambang batas destinasi wisata talaga biru,” JUSTE Journal Sci. Technol., vol. 2, no. 1, pp. 52–58, Oct. 2021, doi: 10.51135/justevol2issue1page52-58.
M. N. Dalengkade et al., “Visit profiles and tourism destination thresholds using polynomial and Malthusian,” BAREKENG J. Ilmu Mat. dan Terap., vol. 16, no. 1, pp. 113–120, Mar. 2022, doi: 10.30598/barekengvol16iss1pp113-120.
T. Waezizadeh, A. Mehrpooya, M. Rezaeizadeh, and S. Yarahmadian, “Mathematical models for the effects of hypertension and stress on kidney and their uncertainty,” Math. Biosci., vol. 305, pp. 77–95, Nov. 2018, doi: 10.1016/j.mbs.2018.08.013.
W. O. Kermack and A. G. McKendrick, “A contribution to the mathematical theory of epidemics,” Proc. R. Soc. London. Ser. A, Contain. Pap. a Math. Phys. Character, vol. 115, no. 772, pp. 700–721, Aug. 1927, doi: 10.1098/rspa.1927.0118.
N. T. J. Bailey, The mathematical theory of Infectious Diseases and its Applications, Second Edi. London: Charles Griffin & Company LTD, 1975.
R. Detels, R. Beaglehole, M. A. Lansang, and M. Gulliford, Oxford Textbook of Public Health, no. May. Oxford University Press, 2009. doi: 10.1093/med/9780199218707.001.0001.
M. J. Keeling and P. Rohani, Modeling Infectioous Diseases: In Human and Animals. United Kingdom: Princeton University Press, 2008.
T. C. Reluga, “Game theory of social distancing in response to an epidemic,” PLoS Comput. Biol., vol. 6, no. 5, p. e1000793, May 2010, doi: 10.1371/journal.pcbi.1000793.
S. E. Eikenberry et al., “To mask or not to mask: Modeling the potential for face mask use by the general public to curtail the COVID-19 pandemic,” Infect. Dis. Model., vol. 5, pp. 293–308, 2020, doi: 10.1016/j.idm.2020.04.001.
S. Towers, K. Vogt Geisse, Y. Zheng, and Z. Feng, “Antiviral treatment for pandemic influenza: Assessing potential repercussions using a seasonally forced SIR model,” J. Theor. Biol., vol. 289, no. 1, pp. 259–268, Nov. 2011, doi: 10.1016/j.jtbi.2011.08.011.
K. C. Ang, “A simple model for a SARS epidemic,” Teach. Math. its Appl., vol. 23, no. 4, pp. 181–188, Dec. 2004, doi: 10.1093/teamat/23.4.181.
N. C. Grassly and C. Fraser, “Mathematical models of infectious disease transmission,” Nat. Rev. Microbiol., vol. 6, no. 6, pp. 477–487, Jun. 2008, doi: 10.1038/nrmicro1845.
T. P. Dreyer, Modelling with Ordinary Differential Equations. Boca Raton: CRC Press, 1993.
F. R. Giordano, W. P. Fox, and S. B. Horton, A First Course in Mathematical Modeling, Fifth Edit. USA: Richard Stratton, 2014.
D. A. Lawson, “Stopping distances: an excellent example of empirical modelling,” Teach. Math. its Appl., vol. 20, no. 2, pp. 66–74, Jun. 2001, doi: 10.1093/teamat/20.2.66.
Z. Wilstein, D. M. Alligood, V. L. McLure, and A. C. Miller, “Mathematical model of hypertension-induced arterial remodeling: A chemo-mechanical approach,” Math. Biosci., vol. 303, no. May, pp. 10–25, Sep. 2018, doi: 10.1016/j.mbs.2018.05.002.
A. Tsamis and N. Stergiopulos, “Arterial remodeling in response to hypertension using a constituent-based model,” Am. J. Physiol. Circ. Physiol., vol. 293, no. 5, pp. H3130–H3139, Nov. 2007, doi: 10.1152/ajpheart.00684.2007.
A. Tsamis, N. Stergiopulos, and A. Rachev, “A structure-based model of arterial remodeling in response to sustained hypertension,” J. Biomech. Eng., vol. 131, no. 10, pp. 1–8, Oct. 2009, doi: 10.1115/1.3192142.
C. Castillo-Chavez, S. Fridman, and X. Luo, “Stochastic and deterministic models in epidemiology,” in World Congress of Nonlinear Analysts ’92, DE GRUYTER, 1996, pp. 3211–3226. doi: 10.1515/9783110883237.3211.
D. Olabode, J. Culp, A. Fisher, A. Tower, D. Hull-Nye, and X. Wang, “Deterministic and stochastic models for the epidemic dynamics of COVID-19 in Wuhan, China,” Math. Biosci. Eng., vol. 18, no. 1, pp. 950–967, 2021, doi: 10.3934/mbe.2021050.
E. Pelinovsky, A. Kurkin, O. Kurkina, M. Kokoulina, and A. Epifanova, “Logistic equation and COVID-19,” Chaos, Solitons & Fractals, vol. 140, p. 110241, Nov. 2020, doi: 10.1016/j.chaos.2020.110241.
E. Aviv-Sharon and A. Aharoni, “Generalized logistic growth modeling of the COVID-19 pandemic in Asia,” Infect. Dis. Model., vol. 5, pp. 502–509, 2020, doi: 10.1016/j.idm.2020.07.003.
N. Balak et al., “A simple mathematical tool to forecast COVID-19 cumulative case numbers,” Clin. Epidemiol. Glob. Heal., vol. 12, no. January, p. 100853, Oct. 2021, doi: 10.1016/j.cegh.2021.100853.
G. K. Mutua, C. G. Ngari, G. G. Muthuri, and D. M. Kitavi, “Mathematical modeling and simulating of Helicobacter pylori treatment and transmission implications on stomach cancer dynamics,” Commun. Math. Biol. Neurosci., vol. 2022, no. August, 2022, doi: 10.28919/cmbn/7542.
Copyright (c) 2025 Mario Nikolaus Dalengkade, Martina Hayati, Dwi Rahayu Pujiastuti
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this Journal agree to the following terms:
- Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
- Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
- Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.
1.gif)
