Mathematical Modeling and Optimal Control Analysis on Sedentary Behavior and Physical Activity in Relation to Cardiovascular Disease (CVD)

Lawal Jibril; Opeyemi Odetunde

doi:doi:10.11648/j.bsi.20200504.13

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Mathematical Modeling and Optimal Control Analysis on Sedentary Behavior and Physical Activity in Relation to Cardiovascular Disease (CVD)

Lawal Jibril, Opeyemi Odetunde

Published in Biomedical Statistics and Informatics (Volume 5, Issue 4)

Received: 5 November 2020 Accepted: 21 November 2020 Published: 31 December 2020

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Abstract

Cardiovascular diseases (CVDs) have remained the leading causes of global death in the last 16 years which is the cause of mortality of 17.7 million people every year. Nowadays, people live in a time where sitting takes up the majority of their daily affairs. The sedentary behavior for prolonged periods of time can leads to a problem of deadly disease such as heart disease, obesity, and diabetes. In this paper a deterministic model for the effects of prolonged sitting is designed. The model, which consists of three ordinary differentials equations is developed and analyzed to study the optimal control analysis on sedentary behavior, physical activity in relation to cardiovascular disease (CVD) in a community. The solutions of the model uniquely exist, nonnegative for all t ≥ 0 with nonnegative initial conditions in R³₊, and bounded in a region Ω_N. The basic reproduction number which measures the relationship threshold is presented. The model was extended and optimal control theory was applied to examine optimal strategies for controlling or eradicating the new cases of CVD that may be borne due to a life of inactivity. The control measures comprises of education or sensitization u₁, living a healthy lifestyle (good nutrition, weight management) u₂, and getting plenty of physical activity u₃. The impact of using possible combinations of the three intervention strategies was investigated and analyzed. The results of the optimal control model using Pontryagin maximum principle (PMP) revealed that combination of education or sensitization with any other control strategy yields better result to reduce or eradicate the risk of new cases of CVD from sedentary lifestyle.

Published in	Biomedical Statistics and Informatics (Volume 5, Issue 4)
DOI	10.11648/j.bsi.20200504.13
Page(s)	87-99
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Deterministic Model, Physical Activity, Sedentary Behavior, Cardiovascular Disease, Optimal Control Analysis

References

[1]	ADAPTS (2019). 6-strategies-for-reducing-the-risk-of-prolonged-sitting-at-work, URL: https://www.adaptergonomics.com/canada/6-strategies-for-reducing-the-risk-of-prolonged-sitting-at-work/assessed.
[2]	A. H. A. (2019). American Heart Association. URL: https://Www. Heart. Org/En/Health-Topics/Consumer-Healthcare/What-Is-Cardiovascular-Disease/Family-History-And-Heart-Disease-Stroke.
[3]	V. Bindu, K. R. Padma, C. Madhuri, D. Sarada (2019). A Study On Coronary Heart Disease Prevention-Nutritional Status, Dietary Patterns and Life Stlye Management, International Journal of Scientific & Technology Research 8 (11).
[4]	D. Dunstan, G. Healy, N. Owen, J. Salmon, N. Ridgers, T. Okely, D. Cliff, M. Daley, A. Bauman (2019). Prolonged sitting. In: Blueprint for an Active Australia. 3rd ed. Melbourne: National Heart Foundation of Australia.
[5]	HRIASIA (2019). Far-Reaching-Business-Implications-Of-A-Sedentary-Workforce-Do-You-Encourage-Prolonged-Sitting https://www.hrinasia.com/people-development/far-reaching-business-implications-of-a-sedentary-workforce-do-you-encourage-prolonged-sitting/.
[6]	M. O. Ibrahim, S. T. Akinyemi, M. M. Dogo, and N. G Bakare (2015). Mathematical Modeling of a Stage Progression HIV/ AIDS Model with Control Measures, Journal of Nigerian Ass of Math Physics, vol 9 151–162.
[7]	L. Jibril and A. U. Moyi (2019). Differential Transform Method for the Vaccination Model of the cholera Carrier, International Research Journal of Engineering and Technology (IRJET) 6 (11) 2379–2386.
[8]	M. D. W. Kraus (2015). Family History and Heart Disease, Stroke, American Heart Association. https://www.heart.org/en/health-topics/consumer-healthcare/what-is-cardiovascular-disease/family-history-and-heart-disease-stroke.
[9]	S. Lenhart and J. T. Workman (2007). Optimal Control applied to biological Models. United States of America: Chapman & Hall/CRC.
[10]	M. D. Michos (2015, July 17). Health. Retrieved from John Hopkins Medicine: URL: https://www.hopkinsmedicine.org/health/wellness-and-prevention/sitting-disease-how-a-sedentary-lifestyle-affects-heart-health.
[11]	N. H. S (2018). URL: https://Www.nhs. Uk/Conditions/Cardiovascular-Disease/.
[12]	L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelize and E. F. Mischenko (1962). The mathematical theory of optimal processes. New York: Wiley.
[13]	D. Shambhavi and K. Bansal (2019). A study of cardiovascular risk behaviour among medical students in a medical college, Gurugram Haryana”, International Journal of Current Research, 11, (11), 8451-8453.
[14]	J. P. Thyfault, D. Mengmeng, W. E Kraus, J. A. Levine, and F. W. Booth (2015). Physiology of Sedentary Behavior and Its Relationship to Health Outcomes, Med Sci Sports Exerc, 47 (6): 1301–1305.
[15]	UTKATA (2019). What-Sitting-all-Day-does-toyour-Body-and-how-to-Reversethe-Harmful-Effects, URL: https://utkatayoga.com/what-sitting-all-day-does-to-your-body-and-how-to-reverse-the-harmful-effects/.
[16]	Wikipedia (2014). Sedentary Life styes, URL: https://www.lifespanfitness.cm/workplace/resources/articles/sitting-all-day-is-taking-a-toll- on-your-body.
[17]	World Health Organisation. URL:https://www.who.int/news-room/fact-sheets/detail/cardiovascular-diseases-(cvds).
[18]	W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character 115 (1927) 700–721.

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APA Style

Lawal Jibril, Opeyemi Odetunde. (2020). Mathematical Modeling and Optimal Control Analysis on Sedentary Behavior and Physical Activity in Relation to Cardiovascular Disease (CVD). Biomedical Statistics and Informatics, 5(4), 87-99. https://doi.org/10.11648/j.bsi.20200504.13

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ACS Style

Lawal Jibril; Opeyemi Odetunde. Mathematical Modeling and Optimal Control Analysis on Sedentary Behavior and Physical Activity in Relation to Cardiovascular Disease (CVD). Biomed. Stat. Inform. 2020, 5(4), 87-99. doi: 10.11648/j.bsi.20200504.13

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AMA Style

Lawal Jibril, Opeyemi Odetunde. Mathematical Modeling and Optimal Control Analysis on Sedentary Behavior and Physical Activity in Relation to Cardiovascular Disease (CVD). Biomed Stat Inform. 2020;5(4):87-99. doi: 10.11648/j.bsi.20200504.13

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@article{10.11648/j.bsi.20200504.13,
  author = {Lawal Jibril and Opeyemi Odetunde},
  title = {Mathematical Modeling and Optimal Control Analysis on Sedentary Behavior and Physical Activity in Relation to Cardiovascular Disease (CVD)},
  journal = {Biomedical Statistics and Informatics},
  volume = {5},
  number = {4},
  pages = {87-99},
  doi = {10.11648/j.bsi.20200504.13},
  url = {https://doi.org/10.11648/j.bsi.20200504.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bsi.20200504.13},
  abstract = {Cardiovascular diseases (CVDs) have remained the leading causes of global death in the last 16 years which is the cause of mortality of 17.7 million people every year. Nowadays, people live in a time where sitting takes up the majority of their daily affairs. The sedentary behavior for prolonged periods of time can leads to a problem of deadly disease such as heart disease, obesity, and diabetes. In this paper a deterministic model for the effects of prolonged sitting is designed. The model, which consists of three ordinary differentials equations is developed and analyzed to study the optimal control analysis on sedentary behavior, physical activity in relation to cardiovascular disease (CVD) in a community. The solutions of the model uniquely exist, nonnegative for all t ≥ 0 with nonnegative initial conditions in R3+, and bounded in a region ΩN. The basic reproduction number which measures the relationship threshold is presented. The model was extended and optimal control theory was applied to examine optimal strategies for controlling or eradicating the new cases of CVD that may be borne due to a life of inactivity. The control measures comprises of education or sensitization u1, living a healthy lifestyle (good nutrition, weight management) u2, and getting plenty of physical activity u3. The impact of using possible combinations of the three intervention strategies was investigated and analyzed. The results of the optimal control model using Pontryagin maximum principle (PMP) revealed that combination of education or sensitization with any other control strategy yields better result to reduce or eradicate the risk of new cases of CVD from sedentary lifestyle.},
 year = {2020}
}

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TY  - JOUR
T1  - Mathematical Modeling and Optimal Control Analysis on Sedentary Behavior and Physical Activity in Relation to Cardiovascular Disease (CVD)
AU  - Lawal Jibril
AU  - Opeyemi Odetunde
Y1  - 2020/12/31
PY  - 2020
N1  - https://doi.org/10.11648/j.bsi.20200504.13
DO  - 10.11648/j.bsi.20200504.13
T2  - Biomedical Statistics and Informatics
JF  - Biomedical Statistics and Informatics
JO  - Biomedical Statistics and Informatics
SP  - 87
EP  - 99
PB  - Science Publishing Group
SN  - 2578-8728
UR  - https://doi.org/10.11648/j.bsi.20200504.13
AB  - Cardiovascular diseases (CVDs) have remained the leading causes of global death in the last 16 years which is the cause of mortality of 17.7 million people every year. Nowadays, people live in a time where sitting takes up the majority of their daily affairs. The sedentary behavior for prolonged periods of time can leads to a problem of deadly disease such as heart disease, obesity, and diabetes. In this paper a deterministic model for the effects of prolonged sitting is designed. The model, which consists of three ordinary differentials equations is developed and analyzed to study the optimal control analysis on sedentary behavior, physical activity in relation to cardiovascular disease (CVD) in a community. The solutions of the model uniquely exist, nonnegative for all t ≥ 0 with nonnegative initial conditions in R3+, and bounded in a region ΩN. The basic reproduction number which measures the relationship threshold is presented. The model was extended and optimal control theory was applied to examine optimal strategies for controlling or eradicating the new cases of CVD that may be borne due to a life of inactivity. The control measures comprises of education or sensitization u1, living a healthy lifestyle (good nutrition, weight management) u2, and getting plenty of physical activity u3. The impact of using possible combinations of the three intervention strategies was investigated and analyzed. The results of the optimal control model using Pontryagin maximum principle (PMP) revealed that combination of education or sensitization with any other control strategy yields better result to reduce or eradicate the risk of new cases of CVD from sedentary lifestyle.
VL  - 5
IS  - 4
ER  -

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Author Information

Lawal Jibril

Department of Mathematical Sciences, Faculty of Science, Federal University Gusau, Gusau, Nigeria
Opeyemi Odetunde

Department of Mathematics, Faculty of Physical Science, University of Ilorin, Ilorin, Nigeria

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APA Style

Lawal Jibril, Opeyemi Odetunde. (2020). Mathematical Modeling and Optimal Control Analysis on Sedentary Behavior and Physical Activity in Relation to Cardiovascular Disease (CVD). Biomedical Statistics and Informatics, 5(4), 87-99. https://doi.org/10.11648/j.bsi.20200504.13

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ACS Style

Lawal Jibril; Opeyemi Odetunde. Mathematical Modeling and Optimal Control Analysis on Sedentary Behavior and Physical Activity in Relation to Cardiovascular Disease (CVD). Biomed. Stat. Inform. 2020, 5(4), 87-99. doi: 10.11648/j.bsi.20200504.13

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AMA Style

Lawal Jibril, Opeyemi Odetunde. Mathematical Modeling and Optimal Control Analysis on Sedentary Behavior and Physical Activity in Relation to Cardiovascular Disease (CVD). Biomed Stat Inform. 2020;5(4):87-99. doi: 10.11648/j.bsi.20200504.13

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@article{10.11648/j.bsi.20200504.13,
  author = {Lawal Jibril and Opeyemi Odetunde},
  title = {Mathematical Modeling and Optimal Control Analysis on Sedentary Behavior and Physical Activity in Relation to Cardiovascular Disease (CVD)},
  journal = {Biomedical Statistics and Informatics},
  volume = {5},
  number = {4},
  pages = {87-99},
  doi = {10.11648/j.bsi.20200504.13},
  url = {https://doi.org/10.11648/j.bsi.20200504.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bsi.20200504.13},
  abstract = {Cardiovascular diseases (CVDs) have remained the leading causes of global death in the last 16 years which is the cause of mortality of 17.7 million people every year. Nowadays, people live in a time where sitting takes up the majority of their daily affairs. The sedentary behavior for prolonged periods of time can leads to a problem of deadly disease such as heart disease, obesity, and diabetes. In this paper a deterministic model for the effects of prolonged sitting is designed. The model, which consists of three ordinary differentials equations is developed and analyzed to study the optimal control analysis on sedentary behavior, physical activity in relation to cardiovascular disease (CVD) in a community. The solutions of the model uniquely exist, nonnegative for all t ≥ 0 with nonnegative initial conditions in R3+, and bounded in a region ΩN. The basic reproduction number which measures the relationship threshold is presented. The model was extended and optimal control theory was applied to examine optimal strategies for controlling or eradicating the new cases of CVD that may be borne due to a life of inactivity. The control measures comprises of education or sensitization u1, living a healthy lifestyle (good nutrition, weight management) u2, and getting plenty of physical activity u3. The impact of using possible combinations of the three intervention strategies was investigated and analyzed. The results of the optimal control model using Pontryagin maximum principle (PMP) revealed that combination of education or sensitization with any other control strategy yields better result to reduce or eradicate the risk of new cases of CVD from sedentary lifestyle.},
 year = {2020}
}

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TY  - JOUR
T1  - Mathematical Modeling and Optimal Control Analysis on Sedentary Behavior and Physical Activity in Relation to Cardiovascular Disease (CVD)
AU  - Lawal Jibril
AU  - Opeyemi Odetunde
Y1  - 2020/12/31
PY  - 2020
N1  - https://doi.org/10.11648/j.bsi.20200504.13
DO  - 10.11648/j.bsi.20200504.13
T2  - Biomedical Statistics and Informatics
JF  - Biomedical Statistics and Informatics
JO  - Biomedical Statistics and Informatics
SP  - 87
EP  - 99
PB  - Science Publishing Group
SN  - 2578-8728
UR  - https://doi.org/10.11648/j.bsi.20200504.13
AB  - Cardiovascular diseases (CVDs) have remained the leading causes of global death in the last 16 years which is the cause of mortality of 17.7 million people every year. Nowadays, people live in a time where sitting takes up the majority of their daily affairs. The sedentary behavior for prolonged periods of time can leads to a problem of deadly disease such as heart disease, obesity, and diabetes. In this paper a deterministic model for the effects of prolonged sitting is designed. The model, which consists of three ordinary differentials equations is developed and analyzed to study the optimal control analysis on sedentary behavior, physical activity in relation to cardiovascular disease (CVD) in a community. The solutions of the model uniquely exist, nonnegative for all t ≥ 0 with nonnegative initial conditions in R3+, and bounded in a region ΩN. The basic reproduction number which measures the relationship threshold is presented. The model was extended and optimal control theory was applied to examine optimal strategies for controlling or eradicating the new cases of CVD that may be borne due to a life of inactivity. The control measures comprises of education or sensitization u1, living a healthy lifestyle (good nutrition, weight management) u2, and getting plenty of physical activity u3. The impact of using possible combinations of the three intervention strategies was investigated and analyzed. The results of the optimal control model using Pontryagin maximum principle (PMP) revealed that combination of education or sensitization with any other control strategy yields better result to reduce or eradicate the risk of new cases of CVD from sedentary lifestyle.
VL  - 5
IS  - 4
ER  -

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