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Optimal nutritional intake for fetal growth
1. | Department of Mathematics, Mahidol University, Bangkok 10400, Thailand & National Research Centre for Growth and Development, Auckland, New Zealand |
2. | National Research Centre for Growth and Development & Institute of Information and Mathematical Sciences, Massey University, Private Bag 102904, Albany, Auckland |
3. | Institute of Information and Mathematical Sciences, Massey University, Private Bag 102904, Albany, Auckland, New Zealand |
4. | Department of Mathematics, Mahidol University, Bangkok 10400, Thailand & Center of Excellence in Mathematics,, PERDO Commission on Higher Education, Si Ayudhya Rd., Bangkok 10400, New Zealand |
References:
[1] |
C. W. Clark, "Bioeconomics: The Optimal Management of Renewable Resources," Wiley, New York, 1976. |
[2] |
H. R. Joshi, Optimal control of an HIV immunology model, Optim. Control Appl. Methods, 23 (2002), 199-213.
doi: 10.1002/oca.710. |
[3] |
E. Jung, S. Lenhart and Z. Feng, Optimal control of treatments in a two-strain tuberculosis model, Discrete and Continuous Dynamical Systems-Series B, 2 (2002), 473-482.
doi: 10.3934/dcdsb.2002.2.473. |
[4] |
K. L. Gatford, J. A. Owens, S. Li, T. J. M. Moss, J. P. Newnham, J. R. G. Challis and D. M. Sloboda, Repeated betamethasone treatment of pregnant sheep programspersistent reductions in circulating IGF-I and IGF-binding proteins in progeny, Am. J. Physiol. Endocrinol. Metab., 295 (2008), 170-178.
doi: 10.1152/ajpendo.00047.2008. |
[5] |
D. Kirschner, S. Lenhart and S. Serbis, Optimal control of the chemotherapy of HIV, J. Math. Biol., 35 (1997), 775-792.
doi: 10.1007/s002850050076. |
[6] |
S. Lenhart and J. T. Workman, Optimal control applied to biological models, in "Chapman & Hall/CRC Mathematical and Computational Biology Series," Chapman & Hall/CRC, Boca Raton, FL, 2007. |
[7] |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelize and E. F. Mishchenko, "The Mathematical Theory of Optimal Processes" (ed. L. W. Neustadt), Interscience Publishers John Wiley & Sons, Inc., New York-London, 1962. |
[8] |
D. A. Redmer, J. M. Wallace and L. P. Reynolds, Effect of nutrient intake during pregnancy on fetal and placental growth and vascular development, Domestic Animal Endocrinology, 27 (2004), 199-217.
doi: 10.1016/j.domaniend.2004.06.006. |
[9] |
G. Wu, F. W. Bazer, T. A. Cudd, C. J. Meininger and T. E. Spencer, Maternal nutrition and fetal development, Journal of Nutrition, 134 (2004), 2169-2172. |
[10] |
G. Wu, F. W. Bazer, J. M. Wallace and T. E. Spencer, Board-invited review: Intraurine growth retardation: Implications for the animal sciences, Journal of Animal Science, 84 (2006), 2316-2337.
doi: 10.2527/jas.2006-156. |
[11] |
G. Zaman, Y. H. Kang and I. H. Jung, Optimal vaccination and treatment in the SIR epidemic model, Proc. KSIAM, 3 (2007), 31-33. |
show all references
References:
[1] |
C. W. Clark, "Bioeconomics: The Optimal Management of Renewable Resources," Wiley, New York, 1976. |
[2] |
H. R. Joshi, Optimal control of an HIV immunology model, Optim. Control Appl. Methods, 23 (2002), 199-213.
doi: 10.1002/oca.710. |
[3] |
E. Jung, S. Lenhart and Z. Feng, Optimal control of treatments in a two-strain tuberculosis model, Discrete and Continuous Dynamical Systems-Series B, 2 (2002), 473-482.
doi: 10.3934/dcdsb.2002.2.473. |
[4] |
K. L. Gatford, J. A. Owens, S. Li, T. J. M. Moss, J. P. Newnham, J. R. G. Challis and D. M. Sloboda, Repeated betamethasone treatment of pregnant sheep programspersistent reductions in circulating IGF-I and IGF-binding proteins in progeny, Am. J. Physiol. Endocrinol. Metab., 295 (2008), 170-178.
doi: 10.1152/ajpendo.00047.2008. |
[5] |
D. Kirschner, S. Lenhart and S. Serbis, Optimal control of the chemotherapy of HIV, J. Math. Biol., 35 (1997), 775-792.
doi: 10.1007/s002850050076. |
[6] |
S. Lenhart and J. T. Workman, Optimal control applied to biological models, in "Chapman & Hall/CRC Mathematical and Computational Biology Series," Chapman & Hall/CRC, Boca Raton, FL, 2007. |
[7] |
L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelize and E. F. Mishchenko, "The Mathematical Theory of Optimal Processes" (ed. L. W. Neustadt), Interscience Publishers John Wiley & Sons, Inc., New York-London, 1962. |
[8] |
D. A. Redmer, J. M. Wallace and L. P. Reynolds, Effect of nutrient intake during pregnancy on fetal and placental growth and vascular development, Domestic Animal Endocrinology, 27 (2004), 199-217.
doi: 10.1016/j.domaniend.2004.06.006. |
[9] |
G. Wu, F. W. Bazer, T. A. Cudd, C. J. Meininger and T. E. Spencer, Maternal nutrition and fetal development, Journal of Nutrition, 134 (2004), 2169-2172. |
[10] |
G. Wu, F. W. Bazer, J. M. Wallace and T. E. Spencer, Board-invited review: Intraurine growth retardation: Implications for the animal sciences, Journal of Animal Science, 84 (2006), 2316-2337.
doi: 10.2527/jas.2006-156. |
[11] |
G. Zaman, Y. H. Kang and I. H. Jung, Optimal vaccination and treatment in the SIR epidemic model, Proc. KSIAM, 3 (2007), 31-33. |
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