Optimal Control Strategies for the Population Management of the Bali Starling
A Mathematical Modeling Approach
DOI:
https://doi.org/10.5614/cbms.2025.8.2.3Keywords:
Population dynamic, Bali Starling, optimal control strategy, endangered species populations, math-ematical modelingAbstract
The Bali Starling (Leucopsar rothschildi), an endemic species of Bali, faces severe threats from habitat loss, poaching, and environmental changes, necessitating effective conservation strategies. This study presents a mathematical model to describe the population dynamics of the Bali Starling within the breeding center at USS Tegal Bunder, TNBB, integrating optimal control theory to improve conservation efforts. The model incorporates key biological factors such as growth, transfer, and habituation processes, and utilizes Pontryagin?s Maximum Principle to determine an optimal control strategy that balances population sustainability with resource efficiency. Numerical simulations compare controlled and uncontrolled scenarios, highlighting the impact of different control cost weights (q) on population management. The results suggest that moderate control interventions (q = 0.06 ? 0.10) are most effective, ensuring sustainable population growth while min- imizing intervention costs. These findings provide valuable insights for optimizing captive breeding programs and offer a scientific basis for adaptive conservation strategies to protect endangered species like the Bali Starling.
References
Aalipour, A., Kebriaei, H. and Ramezani, M., Analytical optimal solution of perimeter traffic flow control based on MFD dynamics: A Pontryagin?s maximum principle approach, IEEE Transactions on Intelligent Transportation Systems, 20(9), pp. 3224-3234, 2018.
Acquistapace, P. and Bartaloni, F., Optimal control with state constraint and non-concave dynamics: a model arising in economic growth, Applied Mathematics & Optimization, 76(2), pp. 323-373, 2017.
Ardhana, I.P.G. and Rukmana, N., Keberadaan Jalak Bali (Leucopsar rothschildi Stresemann 1912) di Taman Nasional Bali Barat, Simbiosis, 1(1), 2017.
Baker, C.M. and Bode, M., Recent advances of quantitative modeling to support invasive species eradication on islands, Conservation Science and Practice, 3(2), p. e246, 2021.
Caswell, H., Matrix population models, Sinauer, 2001.
Caughley, G., Sampling in aerial survey, The Journal of Wildlife Management, pp. 605-615, 1977.
Cenci, S. and Saavedra, S., Structural stability of nonlinear population dynamics, Physical Review E, 97(1), p. 012401, 2018.
Cesari, L., Optimization?theory and applications: problems with ordinary differential equations (Vol. 17), Springer Science & Business Media, 2012.
Clarke, F., Functional analysis, calculus of variations and optimal control (Vol. 264, p. 591), London: Springer, 2013.
Mat Daud, A.A., Mathematical modeling and stability analysis of population dynamics, In SEAMS School on Dynamical Systems and Bifurcation Analysis (pp. 3-13), Singapore: Springer Singapore, 2018.
Dontchev, A.L., Kolmanovsky, I., Krastanov, M.I., Nicotra, M. and Veliov, V.M., Lipschitz stability in discretized optimal control with application to SQP, SIAM Journal on Control and Optimization, 57(1), pp. 468-489, 2019.
Earnhardt, J.M., Thompson, S.D. and Faust, L.J., Extinction risk assessment for the species survival plan (SSP) population of the Bali mynah (Leucopsar rothschildi), Zoo Biology: Published in affiliation with the American Zoo and Aquarium Association, 28(3), pp. 230-252, 2009.
Feng, Z., Li, F., Lv, Y. and Zhang, S., A note on Cauchy-Lipschitz-Picard theorem, Journal of Inequalities and Applications, 2016(1), p. 271, 2016.
Gandhiadi, G.K., Jayanegara, K. and Dharmawan, K., Modeling and Analysis of the Dynamic Model of Bali Starling (Leucopsar Rothschildi) Breeding in West Bali National Park, JTAM (Jurnal Teori dan Aplikasi Matematika), 7(4), pp. 1043-1053, 2023.
Gelashvili, K., The existence of optimal control on the basis of Weierstrass?s theorem, Journal of Mathematical Sciences, 177(3), pp. 373-382, 2011.
Guiver, C., Logemann, H., Rebarber, R., Bill, A., Tenhumberg, B., Hodgson, D. and Townley, S., Integral control for population management. Journal of Mathematical Biology, 70(5), pp. 1015-1063, 2015.
Guiver, C., Mueller, M., Hodgson, D. and Townley, S., Robust set-point regulation for ecological models with multiple management goals, Journal of Mathematical Biology, 72(6), pp. 1467-1529, 2016.
Jepson, P.R., Saving a species threatened by trade: a network study of Bali starling Leucopsar rothschildi conservation, Oryx, 50(3), pp. 480-488, 2016.
Jepson, P. and Barua, M., A theory of flagship species action, Conservation and Society, 13(1), pp. 95-104, 2015.
Jian, S. and Ching-Yuan, Y., On stability theory of population systems and critical fertility rates, Mathematical Modelling, 2(2), pp. 109-121, 1981.
Kirk, D.E., Optimal control theory: an introduction, Courier Corporation, 2004.
Lacy, R.C. and Pollak, J.P., VORTEX: a stochastic simulation of the extinction process, Chicago Zoological Society, 2014.
Lande, R., Engen, S. and Saether, B.E., Stochastic population dynamics in ecology and conservation, Oxford University Press, USA, 2003.
Lenhart, S. and Workman, J.T., Optimal control applied to biological models, Chapman and Hall/CRC, 2007.
Leal-Ram?rez, C., Castillo, O., Melin, P. and Rodr?guez-D?az, A., Simulation of the bird age-structured population growth based on an interval type-2 fuzzy cellular structure, Information Sciences, 181(3), pp. 519-535, 2011.
Misztela, A., Representation of Hamilton?Jacobi equation in optimal control theory with unbounded control set, Journal of Optimization Theory and Applications, 185(2), pp. 361-383, 2020.
Murray, J.D., Mathematical biology: I. An introduction (Vol. 17), Springer Science & Business Media, 2007.
Noerdjito, M., Roemantyo, R. and Sumampau, T., Merekonstruksi Habitat Curik Bali Leucopsar rothschildi Stresemann, 1912 di Bali Bagian Barat, Jurnal Biologi Indonesia, 7(2), 2017.
Pedregal, P. and Tiago, J., Existence results for optimal control problems with some special nonlinear dependence on state and control, SIAM Journal on Control and Optimization, 48(2), pp. 415-437, 2009.
Pramatana, F., Prasetyo, L.B. and Rushayati, S.B., The habitat susceptibility of Bali Starling (Leucopsar rothschildi stresemann > 1912) based on forest fire vulnerability mappin in West Bali National Park, IOP Conference Series: Earth and Environmental Science, 91(1), p. 012003, 2017,
Pramatana, F., Hernowo, J.B. and Prasetyo, L.B., Population and habitat suitability index model of Bali Starling (Leucopsar rothschildi) in West Bali National Park, Jurnal Sylva Lestari, 10(1), pp. 26-38, 2022.
Siegmund, S., Nowak, C. and Dibl?k, J., A generalized Picard-Lindelof theorem, Electronic Journal of Qualitative Theory of Differential Equations, 28(8), pp. 1-8, 2016.
Rosenblueth, J.F., Admissible directions in optimal control under uniqueness assumptions, WSEAS Transactions on Systems and Control, 18, pp. 382-392, 2023.
Spindler, K., Optimal control on Lie groups: theory and applications, WSEAS Trans, Math, 12(5), pp. 531-542, 2013.
Sudaryanto, S., Djohan, T.S., Pudyatmoko, S. and Subagja, J., Behavior of Bali Starling at Bali Barat National Park and Nusa Penida Island, pp. 364-370, 2015.
Sudaryanto, F.X., Pudyatmoko, S., Subagja, J. and Djohan, T.S., The role of awig-awig of traditional village to Bali starling conservation in Nusa Penida Islands, Jurnal Kajian Bali, 9(1), pp. 227-240, 2019.
Sutomo, S., Darma, I.D.P. and Iryadi, R., The dissimilarity in plant species composition of savanna ecosystem along the elevation gradient on Flores Island, East Nusa Tenggara, Indonesia, Biodiversitas Journal of Biological Diversity, 21(2), 2020.
Adesola, O.I., Temilade, M.I., Emmanuel, P.M., Oladele, A.S., Adeyemi, A.G., Sunday, S. and Olumuyiwa, A.S., Mathematical analysis of optimal control of Human Immunodeficiency Virus (HIV) co-infection with Tuberculosis (TB), Asian Research Journal of Current Science, 6(1), pp. 23-53, 2024.
Widyaputra, R., Sistem manajemen proses produksi dan penampilan produksi Jalak Bali (Leucopsar rothschildi) di penangkaran, PhD dissertation, Universitas Airlangga, 2014.
Welsh, M.J., Turner, J.A., Epanchin-Niell, R.S., Monge, J.J., Soliman, T., Robinson, A.P., Kean, J.M., Phillips, C., Stringer, L.D., Vereijssen, J. and Liebhold, A.M., Approaches for estimating benefits and costs of interventions in plant biosecurity across invasion phases, Ecological Applications, 31(5), p. e02319, 2021.
Wei, Q., Song, R., Li, B. and Lin, X., Self-learning optimal control of nonlinear systems, Springer, 2018.
Yaegashi, Y., Yoshioka, H., Unami, K. and Fujihara, M., A singular stochastic control model for sustainable population management of the fish-eating waterfowl Phalacrocorax carbo, Journal of Environmental Management, 219, pp. 18-27, 2018.
Yicang, Z. and Cushing, J.M., Stability conditions for equilibra of nonlinear matrix population models, Journal of Difference Equations and Applications, 4(2), pp. 95-126, 1998.
Zhou, Y., Yang, K., Zhou, K. and Liang, Y., Optimal vaccination policies for an SIR model with limited resources, Acta Biotheoretica, 62(2), pp. 171-181, 2014.
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