| Citation: |
Chathuri T. Sandamali, Wenjing Zhang. MODELING AND ANALYSIS OF SOCIAL OBESITY EPIDEMIC[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 1023-1045. doi: 10.11948/20230282
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MODELING AND ANALYSIS OF SOCIAL OBESITY EPIDEMIC
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Abstract
Overweight and obesity have become a global epidemic due to increasing unhealthy eating habits and sedentary lifestyles. An individual can gain weight excessively through social influence, and understanding its underlying interpersonal dynamics is crucial for effective intervention and prevention programs. By considering the social effects on weight gain, this paper presents a compartment model to describe the social spread of overweight and obesity. Bifurcation analysis suggests that a backward bifurcation exists when the relative hazard of weight regain is a larger value. Strategies for eliminating the overweight and obesity epidemic are provided by analyzing the obesity-free equilibrium globally by incorporating Lyapunov functions and the method of fluctuations. Since the pervasiveness of overweight and obesity in the United States seems to be stabilized, we analyze the local stability of the obesity-endemic equilibrium to establish a condition for the plateau, by applying a matrix theoretic method that utilizes compound matrices. The results suggest that weight loss programs can help maintain the plateau; however, weight loss maintenance programs should be promoted to eliminate the disease.
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Keywords:
- Obesity /
- saddle-node bifurcation /
- bi-stability /
- global stability
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References
[1] A. J. Arenas, G. González-Parra and L. Jódar, Periodic solutions of nonautonomous differential systems modeling obesity population, Chaos, Solitons & Fractals, 2009, 42(2), 1234–1244. [2] I. Bárány and J. Solymosi, Gershgorin disks for multiple eigenvalues of non-negative matrices, in A Journey Through Discrete Mathematics, Springer, 2017, 123–133. [3] N. Becker, The uses of epidemic models, Biometrics, 1979, 295–305. [4] N. Chitnis, J. M. Hyman and J. M. Cushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bulletin of mathematical biology, 2008, 70(5), 1272. doi: 10.1007/s11538-008-9299-0 [5] N. A. Christakis and J. H. Fowler, The spread of obesity in a large social network over 32 years, New England Journal of Medicine, 2007, 357(4), 370–379. PMID: 17652652. doi: 10.1056/NEJMsa066082 [6] A. Datar and N. Nicosia, Assessing social contagion in body mass index, overweight, and obesity Using a natural experiment, JAMA Pediatrics, 2018, 172(3), 239–246. doi: 10.1001/jamapediatrics.2017.4882 [7] K. Ejima, K. Aihara and H. Nishiura, Modeling the obesity epidemic: Social contagion and its implications for control, Theoretical Biology and Medical Modelling, 2013, 10(1), 1–13. doi: 10.1186/1742-4682-10-1 [8] C. Garcia Ulen, M. M. Huizinga, B. Beech and T. A. Elasy, Weight regain prevention, Clinical Diabetes, 2008, 26(3), 100–113. doi: 10.2337/diaclin.26.3.100 [9] W. Gwozdz, A. Sousa-Poza, L. Reisch, et al., Peer effects on obesity in a sample of european children, Economics and Human Biology, 2015, 18, 139–152. doi: 10.1016/j.ehb.2015.05.002 [10] K. D. Hall and S. Kahan, Maintenance of lost weight and long-term management of obesity, Medical Clinics, 2018, 102(1), 183–197. [11] L. Jódar, F. J. Santonja and G. González-Parra, Modeling dynamics of infant obesity in the region of Valencia, Spain, Computers and Mathematics with Applications, 2008, 56(3), 679–689. Mathematical Models in Life Sciences and Engineering. doi: 10.1016/j.camwa.2008.01.011 [12] Y. A. Kuznetsov, I. A. Kuznetsov and Y. Kuznetsov, Elements of Applied Bifurcation Theory, Springer, 1998, 112. [13] C. C. McCluskey and P. V. D. Driessche, Global analysis of two tuberculosis models, Journal of Dynamics and Differential Equations, 2004, 16(1), 139–166. doi: 10.1023/B:JODY.0000041283.66784.3e [14] NCHS, Prevalence of Obesity in the United States 2009–2010, https://www.cdc.gov/nchs/data/databriefs/db82.pdf , 2012.[15] P. Nie, A. Sousa-Poza and X. He, Peer effects on childhood and adolescent obesity in China, China Economic Review, 2015, 35, 47–69. doi: 10.1016/j.chieco.2015.06.002 [16] F. -J. Santonja, R. -J. Villanueva, L. Jódar and G. González-Parra, Mathematical modeling of the social obesity epidemic in the region of Valencia, Spain, Mathematical and Computer Modelling of Dynamical Systems, 2010, 16(1), 23–34. doi: 10.1080/13873951003590149 [17] D. A. Shoham, R. Hammond, H. Rahmandad, et al., Modeling social norms and social influence in obesity, Current Epidemiology Reports, 2015, 2, 71–79. doi: 10.1007/s40471-014-0032-2 [18] Z. Shuai and P. van den Driessche, Global stability of infectious disease models using Lyapunov functions, SIAM Journal on Applied Mathematics, 2013, 73(4), 1513–1532. doi: 10.1137/120876642 [19] N. R. Smith, P. N. Zivich and L. Frerichs, Social influences on obesity: Current knowledge, emerging methods, and directions for future research and practice, Current Nutrition Reports, 2020, 9, 31–41. doi: 10.1007/s13668-020-00302-8 [20] H. R. Thieme, Mathematics in Population Biology, Princeton University Press, 2018, 1. [21] D. M. Thomas, M. Weedermann, B. F. Fuemmeler, et al., Dynamic model predicting overweight, obesity, and extreme obesity prevalence trends, Obesity, 2014, 22(2), 590–597. doi: 10.1002/oby.20520 [22] J. G. Trogdon, J. M. Nonnemaker and J. Pais, Peer effects in adolescent overweight, Journal of Health Economics, 2008, 27(5), 1388–99. doi: 10.1016/j.jhealeco.2008.05.003 [23] J. Tumwiine, J. Mugisha and L. S. Luboobi, A mathematical model for the dynamics of malaria in a human host and mosquito vector with temporary immunity, Applied Mathematics and Computation, 2007, 189(2), 1953–1965. doi: 10.1016/j.amc.2006.12.084 [24] P. van den Driessche, Reproduction numbers of infectious disease models, Infectious Disease Modelling, 2017, 2(3), 288–303. doi: 10.1016/j.idm.2017.06.002 [25] P. van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 2002, 180(1), 29–48. [26] Y. Wang, M. A. Beydoun, J. Min, et al., Has the prevalence of overweight, obesity and central obesity levelled off in the United States? trends, patterns, disparities, and future projections for the obesity epidemic, International Journal of Epidemiology, 2020, 49(3), 810–823. doi: 10.1093/ije/dyz273 [27] WHO, Obesity and Overweight, https://www.who.int/news-room/fact-sheets/detail/obesity-and-overweight , 2020.[28] P. Yu, Closed-form conditions of bifurcation points for general differential equations, International Journal of Bifurcation and Chaos, 2005, 15(4), 1467–1483. doi: 10.1142/S0218127405012582 [29] W. Zhang, Modeling and analysis of the multiannual cholera outbreaks with host-pathogen encounters, International Journal of Bifurcation and Chaos, 2020, 30(8), 2050120. [30] W. Zhang, F. Frascoli and J. Heffernan, Analysis of solutions and disease progressions for a within-host tuberculosis model, Mathematics in Applied Sciences and Engineering, 2020, 1(1), 39–49. [31] W. Zhang and C. T. Sandamali, Modeling and analysis of low-level transmission ZIKV dynamics via a Poisson point process on sexual transmission route, Journal of Applied Analysis & Computation, 2023, 13(2), 1044–1069. -
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Chathuri T. Sandamali, Wenjing Zhang. MODELING AND ANALYSIS OF SOCIAL OBESITY EPIDEMIC[J]. Journal of Applied Analysis & Computation, 2024, 14(2): 1023-1045. doi: 10.11948/20230282
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Figure 1.
Flow diagram of model (2.1) for overweight and obesity dynamics.
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Figure 2.
Backward and forward bifurcation cases are plotted in (a) and (b). The obesity-free equilibrium
$ E_0 $ $ E^\ast $ -
Figure 3.
Time series of unhealthy and healthy weight individuals when (a)
$ m_1=0.02 $ $ m_1=0.035 $ $ (W(0),B(0),R(0))=(0.04,0.001,0.001) $ $ (W(0),B(0),R(0))=(0.01,0.001,0.001) $ $ m_1=0.04 $