Mathematical Model Analysis of Marriage Divorce Incorporating Counselling and Medical Attention

Felicien Habiyaremye

doi:doi:10.11648/j.ajam.20261405.17

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Mathematical Model Analysis of Marriage Divorce Incorporating Counselling and Medical Attention

Felicien Habiyaremye^*

Published in American Journal of Applied Mathematics (Volume 14, Issue 5)

Received: 28 August 2026 Accepted: 10 September 2026 Published: 27 September 2026

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Abstract

This paper has investigated the mathematical model analysis of marriage divorce taking into consideration the effect of counselling and medical attention in order to minimize the divorce cases. The research aimed at developing the deterministic mathematical model of marriage divorce incorporating the counselling and medical attention(treatment), determining the divorce free and endemic equilibrium points, determining the sensitivity analysis and finding numerical simulation. The system of the differential equations of the model was proved to be well posed which showed that the mathematical model of marriage divorce was re-searchable. The differential equations were linearized using Jacobean matrix and It was found that the divorce free equilibrium point to be locally asymptotically stable when the reproduction number is less than one, and divorce endemic equilibrium point to be globally asymptotically unstable when the reproduction number is greater than one, . The sensitivity analysis was done to get the numerical values of the parameters involved in the model. The numerical simulations were done using Runge Kutta fourth order and MATLAB in order to generate the graphs. It was found that the number of divorced individuals reduced as results of individuals got counselling sessions and medical attention (treatment). It was equally observed, the active interaction between married and divorced individuals resulted in the increase of the divorced individuals due to the fact that the reproduction number is greater than one. The number of married individuals increased as a result of individuals got counselling sessions and separated individuals renewed their relationship. This research is of the great help of the community that with good communication, assume responsibility in the family, fidelity as couples, considering diversity in family and avoiding violence of any kind in the family as key factors of avoiding divorce in marriage.

Published in	American Journal of Applied Mathematics (Volume 14, Issue 5)
DOI	10.11648/j.ajam.20261405.17
Page(s)	339-347
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), 2026. Published by Science Publishing Group

Keywords

Mathematical Model, Marriage Divorce, Reproduction Number, Counselling, Medical Attention, Numerical Simulation

References

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[2]	Haileyesus Tessema, Issaka Haruna, Shaibu Ousma, Endeshaw Kassa. Mathematical Model Analysis of Marriage Divorce. Commun. Math. Biol. Neurosci. 2022, 2022: 15. https://doi.org/10.28919/cmbn/6851
[3]	A. Danya, H. A. Bhavithra, S. Sindu Devi. Mathematical Model for Marriage Divorce. https://doi.org/10.52783/anv:28.4492 Vol. 28 no. 7s(2025).
[4]	Nicholas C. Crassly and Christophe Fraser. Mathematical Models of Infectious Disease Transmission. Nature Review Microbiology 6(6), 2008. https://doi.org/10.1038/nrmicro1845
[5]	Herbert W. Hethcote. Qualitative Analysis of Communicable Disease Models. Mathematical Bioscience, 28(3): 335-356, 1976. https:doi.org/10.1016/0025-5564(76)90132.2
[6]	William O. Kermack and Anderson G Mc Kendrick. A Contribution to Mathematical Theory of Epidemics. In proccedings of the Royal Society of London. A Mathematical, Physical and Engineering Sciences, Volume 115, page 700-721. https://doi.org/10.1098/rspa.1927.0118
[7]	Oluwole D. Makinde, Daniel, Daniel S Mgonja and Estomih S Massawe Computational modelling of Cholera Bacteriophage withTreatment.2015. https://doi.org/10.4236/ojepi.2015.5322
[8]	A. A Olaniyi, Analytical Study of the Causal Factors of Divorce in African Homes, Res. Human>Soc. Sci5(2015), 18-29.
[9]	R. Duato, L. Jodar, Mathematical Modelling of the spread of Divorce in Spain, Math. Computer Model. 57(2013), 1732-1737. https://doi.org/10.1016/j.mcm.2011.11.02
[10]	Olowole Daniel Makinde. Adomian Decomposition Approach with Constant Vaccination Strategy. Applied Mathematics and Computation 184(2): 842-848, 2007. https://doi.org/10.1016/j.acm.2006.06.074
[11]	Melinda Moore, Philip Gould, and Barbara, S Keary. Global Urbanization and Impact on Health. International Journal of Hygiene and Environment Health, 206(4-5): 269-278, 2003. https://doi.org/10.1078/1438-4639-00223
[12]	S. M. Blower, H. Dowlatabadi. Sensitivity and Uncertainty Analysis of Complex Models of Disease Transmission: an HIV Model, as an example, Int. Stat. Rev62(1994), 229-243. https://doi.org/10.2307/1403510
[13]	N. O. Mokaya, H. T. Alemmeh, C. G. Muthuri. Mathematical Modelling and Analysis of Corruption of Morals amongst Adolescents with Control Measures in Kenya. Discrete Dyn. Nat. Soc. 2021(2021), 6662185. https://doi.org/10.1155/2021/6662185
[14]	I. Haruna, H. T. Alemneh, G. T. Tilahun. The Effect of Quarantine and Treatment in COVID-19 Transmission: From Mathematical Modelling Perspective. Commun. Math. Biol. NeuroSci 2021(2021), article ID 78. https://doi.org/10.28919/cmbn/6381

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Habiyaremye, F. (2026). Mathematical Model Analysis of Marriage Divorce Incorporating Counselling and Medical Attention. American Journal of Applied Mathematics, 14(5), 339-347. https://doi.org/10.11648/j.ajam.20261405.17

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Habiyaremye, F. Mathematical Model Analysis of Marriage Divorce Incorporating Counselling and Medical Attention. Am. J. Appl. Math. 2026, 14(5), 339-347. doi: 10.11648/j.ajam.20261405.17

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AMA Style

Habiyaremye F. Mathematical Model Analysis of Marriage Divorce Incorporating Counselling and Medical Attention. Am J Appl Math. 2026;14(5):339-347. doi: 10.11648/j.ajam.20261405.17

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@article{10.11648/j.ajam.20261405.17,
  author = {Felicien Habiyaremye},
  title = {Mathematical Model Analysis of Marriage Divorce Incorporating Counselling and Medical Attention},
  journal = {American Journal of Applied Mathematics},
  volume = {14},
  number = {5},
  pages = {339-347},
  doi = {10.11648/j.ajam.20261405.17},
  url = {https://doi.org/10.11648/j.ajam.20261405.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20261405.17},
  abstract = {This paper has investigated the mathematical model analysis of marriage divorce taking into consideration the effect of counselling and medical attention in order to minimize the divorce cases. The research aimed at developing the deterministic mathematical model of marriage divorce incorporating the counselling and medical attention(treatment), determining the divorce free and endemic equilibrium points, determining the sensitivity analysis and finding numerical simulation. The system of the differential equations of the model was proved to be well posed which showed that the mathematical model of marriage divorce was re-searchable. The differential equations were linearized using Jacobean matrix and It was found that the divorce free equilibrium point to be locally asymptotically stable when the reproduction number is less than one, and divorce endemic equilibrium point to be globally asymptotically unstable when the reproduction number is greater than one, . The sensitivity analysis was done to get the numerical values of the parameters involved in the model. The numerical simulations were done using Runge Kutta fourth order and MATLAB in order to generate the graphs. It was found that the number of divorced individuals reduced as results of individuals got counselling sessions and medical attention (treatment). It was equally observed, the active interaction between married and divorced individuals resulted in the increase of the divorced individuals due to the fact that the reproduction number is greater than one. The number of married individuals increased as a result of individuals got counselling sessions and separated individuals renewed their relationship. This research is of the great help of the community that with good communication, assume responsibility in the family, fidelity as couples, considering diversity in family and avoiding violence of any kind in the family as key factors of avoiding divorce in marriage.},
 year = {2026}
}

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TY  - JOUR
T1  - Mathematical Model Analysis of Marriage Divorce Incorporating Counselling and Medical Attention
AU  - Felicien Habiyaremye
Y1  - 2026/09/27
PY  - 2026
N1  - https://doi.org/10.11648/j.ajam.20261405.17
DO  - 10.11648/j.ajam.20261405.17
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 339
EP  - 347
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20261405.17
AB  - This paper has investigated the mathematical model analysis of marriage divorce taking into consideration the effect of counselling and medical attention in order to minimize the divorce cases. The research aimed at developing the deterministic mathematical model of marriage divorce incorporating the counselling and medical attention(treatment), determining the divorce free and endemic equilibrium points, determining the sensitivity analysis and finding numerical simulation. The system of the differential equations of the model was proved to be well posed which showed that the mathematical model of marriage divorce was re-searchable. The differential equations were linearized using Jacobean matrix and It was found that the divorce free equilibrium point to be locally asymptotically stable when the reproduction number is less than one, and divorce endemic equilibrium point to be globally asymptotically unstable when the reproduction number is greater than one, . The sensitivity analysis was done to get the numerical values of the parameters involved in the model. The numerical simulations were done using Runge Kutta fourth order and MATLAB in order to generate the graphs. It was found that the number of divorced individuals reduced as results of individuals got counselling sessions and medical attention (treatment). It was equally observed, the active interaction between married and divorced individuals resulted in the increase of the divorced individuals due to the fact that the reproduction number is greater than one. The number of married individuals increased as a result of individuals got counselling sessions and separated individuals renewed their relationship. This research is of the great help of the community that with good communication, assume responsibility in the family, fidelity as couples, considering diversity in family and avoiding violence of any kind in the family as key factors of avoiding divorce in marriage.
VL  - 14
IS  - 5
ER  -

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Author Information

Felicien Habiyaremye

Department of Computer Science, Information Technology and Business Information Technology, University of Kigali, Kigali, Rwanda

Contact Email

http://orcid.org/0009-0007-4363-6729

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APA Style

Habiyaremye, F. (2026). Mathematical Model Analysis of Marriage Divorce Incorporating Counselling and Medical Attention. American Journal of Applied Mathematics, 14(5), 339-347. https://doi.org/10.11648/j.ajam.20261405.17

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ACS Style

Habiyaremye, F. Mathematical Model Analysis of Marriage Divorce Incorporating Counselling and Medical Attention. Am. J. Appl. Math. 2026, 14(5), 339-347. doi: 10.11648/j.ajam.20261405.17

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AMA Style

Habiyaremye F. Mathematical Model Analysis of Marriage Divorce Incorporating Counselling and Medical Attention. Am J Appl Math. 2026;14(5):339-347. doi: 10.11648/j.ajam.20261405.17

Copy | Download

@article{10.11648/j.ajam.20261405.17,
  author = {Felicien Habiyaremye},
  title = {Mathematical Model Analysis of Marriage Divorce Incorporating Counselling and Medical Attention},
  journal = {American Journal of Applied Mathematics},
  volume = {14},
  number = {5},
  pages = {339-347},
  doi = {10.11648/j.ajam.20261405.17},
  url = {https://doi.org/10.11648/j.ajam.20261405.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20261405.17},
  abstract = {This paper has investigated the mathematical model analysis of marriage divorce taking into consideration the effect of counselling and medical attention in order to minimize the divorce cases. The research aimed at developing the deterministic mathematical model of marriage divorce incorporating the counselling and medical attention(treatment), determining the divorce free and endemic equilibrium points, determining the sensitivity analysis and finding numerical simulation. The system of the differential equations of the model was proved to be well posed which showed that the mathematical model of marriage divorce was re-searchable. The differential equations were linearized using Jacobean matrix and It was found that the divorce free equilibrium point to be locally asymptotically stable when the reproduction number is less than one, and divorce endemic equilibrium point to be globally asymptotically unstable when the reproduction number is greater than one, . The sensitivity analysis was done to get the numerical values of the parameters involved in the model. The numerical simulations were done using Runge Kutta fourth order and MATLAB in order to generate the graphs. It was found that the number of divorced individuals reduced as results of individuals got counselling sessions and medical attention (treatment). It was equally observed, the active interaction between married and divorced individuals resulted in the increase of the divorced individuals due to the fact that the reproduction number is greater than one. The number of married individuals increased as a result of individuals got counselling sessions and separated individuals renewed their relationship. This research is of the great help of the community that with good communication, assume responsibility in the family, fidelity as couples, considering diversity in family and avoiding violence of any kind in the family as key factors of avoiding divorce in marriage.},
 year = {2026}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Model Analysis of Marriage Divorce Incorporating Counselling and Medical Attention
AU  - Felicien Habiyaremye
Y1  - 2026/09/27
PY  - 2026
N1  - https://doi.org/10.11648/j.ajam.20261405.17
DO  - 10.11648/j.ajam.20261405.17
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 339
EP  - 347
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20261405.17
AB  - This paper has investigated the mathematical model analysis of marriage divorce taking into consideration the effect of counselling and medical attention in order to minimize the divorce cases. The research aimed at developing the deterministic mathematical model of marriage divorce incorporating the counselling and medical attention(treatment), determining the divorce free and endemic equilibrium points, determining the sensitivity analysis and finding numerical simulation. The system of the differential equations of the model was proved to be well posed which showed that the mathematical model of marriage divorce was re-searchable. The differential equations were linearized using Jacobean matrix and It was found that the divorce free equilibrium point to be locally asymptotically stable when the reproduction number is less than one, and divorce endemic equilibrium point to be globally asymptotically unstable when the reproduction number is greater than one, . The sensitivity analysis was done to get the numerical values of the parameters involved in the model. The numerical simulations were done using Runge Kutta fourth order and MATLAB in order to generate the graphs. It was found that the number of divorced individuals reduced as results of individuals got counselling sessions and medical attention (treatment). It was equally observed, the active interaction between married and divorced individuals resulted in the increase of the divorced individuals due to the fact that the reproduction number is greater than one. The number of married individuals increased as a result of individuals got counselling sessions and separated individuals renewed their relationship. This research is of the great help of the community that with good communication, assume responsibility in the family, fidelity as couples, considering diversity in family and avoiding violence of any kind in the family as key factors of avoiding divorce in marriage.
VL  - 14
IS  - 5
ER  -

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