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Oh, Chunyoung; M. A, Masud

Optimal intervention strategies for the spread of obesity. (English) Zbl 1435.92037

J. Appl. Math. 2015, Article ID 217808, 9 p. (2015).
Summary: The present study considers a deterministic compartmental model for obesity dynamics. The model exhibits forward bifurcation at basic reproduction number, \(\mathcal{R}_0 = 1\), that is; for \(\mathcal{R}_0 < 1\), obesity is not sustained. However for \(\mathcal{R}_0 > 1\) the model approaches a locally asymptotically stable endemic equilibrium. To control this epidemic and reduce the obesity at the endemic equilibrium, we considered intervention strategies for the spread of overweight and obesity, where Pontryagin’s Maximum Principle is applied. The numerical technique was used to show that there are effective control strategies that include minimizing the social contact rate with the overweight and obese population and campaigning. Numerical results indicated the effects of the two controls (prevention and education/campaigning) to be different. In societies with lower obesity, the social contact rate with the overweight and obese population plays a more prominent role in spreading obesity than lack of educational programs/campaigns. However, for societies with very high obesity burden, education/campaigning proved to be highly effective strategies. Reducing the social contact rate can result in other results such as a depression and an invasion of their individual rights. The appropriate approach to obesity is needed to lower obese societies.

Cited in 2 Documents

MSC:

92C60 Medical epidemiology
92D30 Epidemiology
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References:

[1] WHO
[3] Hammond, R. A.; Levine, R., The economic impact of obesity in the United States, Diabetes, Metabolic Syndrome and Obesity: Targets and Therapy, 3, 285-295 (2010) · doi:10.2147/DMSOTT.S7384
[4] Finkelstein, E. A.; Trogdon, J. G.; Cohen, J. W.; Dietz, W., Annual medical spending attributable to obesity: payer-and service-specific estimates, Health Affairs, 28, 5, w822-w831 (2009) · doi:10.1377/hlthaff.28.5.w822
[5] Christakis, N. A.; Fowler, J. H., The spread of obesity in a large social network over 32 years, The New England Journal of Medicine, 357, 4, 370-379 (2007) · doi:10.1056/nejmsa066082
[6] Jódar, L.; Santonja, F. J.; González-Parra, G., Modeling dynamics of infant obesity in the region of Valencia, Spain, Computers & Mathematics with Applications, 56, 3, 679-689 (2008) · Zbl 1155.92329 · doi:10.1016/j.camwa.2008.01.011
[7] Santonja, F.-J.; Villanueva, R.-J.; Jódar, L.; Gonzalez-Parra, G., Mathematical modelling of social obesity epidemic in the region of Valencia, Spain, Mathematical and Computer Modelling of Dynamical Systems, 16, 1, 23-34 (2010) · Zbl 1298.37080 · doi:10.1080/13873951003590149
[8] Kim, M. S.; Chu, C.; Kim, Y., A note on obesity as epidemic in Korea, Osong Public Health and Research Perspectives, 2, 2, 135-140 (2011) · doi:10.1016/j.phrp.2011.08.004
[9] Aldila, D.; Rarasati, N.; Nuraini, N.; Soewono, E., Optimal control problem of treatment for obesity in a closed population, International Journal of Mathematics and Mathematical Sciences, 2014 (2014) · Zbl 1286.93126 · doi:10.1155/2014/273037
[10] Kim, B. N.; Masud, M. A.; Kim, Y., Optimal implementation of intervention to control the self-harm epidemic, Osong Public Health and Research Perspectives, 5, 6, 315-323 (2014) · doi:10.1016/j.phrp.2014.10.001
[11] Daniel, J., How Mexico got so fat and is now more obese than America
[13] Oh, C., A note on the obesity as an epidemic, Honam Mathematical Journal, 36, 1, 131-139 (2014) · Zbl 1285.92012 · doi:10.5831/hmj.2014.36.1.131
[14] van den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180, 29-48 (2002) · Zbl 1015.92036 · doi:10.1016/S0025-5564(02)00108-6
[15] Lenhart, S.; Workman, J. T., Optimal Control Applied to Biological Models (2007), Chapman & Hall, CRC Press · Zbl 1291.92010
[16] Pontryagin, L. S.; Boltanskii, V. G.; Gamkrelidze, R. V.; Mishchenko, E. F., The Mathematical Theory of Optimal Processes (1962), New York, NY, USA: Wiley, New York, NY, USA · Zbl 0102.32001
[17] Lenhart, S.; Workman, J. T., Optimal Control Applied to Biological Models (2007), Chapman and Hall/CRC · Zbl 1291.92010
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