Optimal Harvesting for a Predator-Prey Agent-Based Model using Difference Equations

Bulletin of Mathematical Biology

Volumn 77, Issue 3, 2015, Pages 434-459

  Oremland, Matthew ^a   Laubenbacher, Reinhard ^b  

^a OHIO STATE UNIVERSITY   (United States)

^b UNIVERSITY OF CONNECTICUT HEALTH CENTER   (United States)

Author keywords

Agent based modeling; Dynamical systems; Heuristic algorithm; Optimization; Statistics

Indexed keywords

ALGORITHM; ANIMAL; BIOLOGICAL MODEL; COMPUTER SIMULATION; FOOD CHAIN; HUMAN; MATHEMATICAL PHENOMENA; POACEAE; RABBIT; SYSTEMS BIOLOGY;

ALGORITHMS; ANIMALS; COMPUTER SIMULATION; FOOD CHAIN; HUMANS; MATHEMATICAL CONCEPTS; MODELS, BIOLOGICAL; POACEAE; RABBITS; SYSTEMS BIOLOGY;

EID: 84939982992     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-014-0060-6     Document Type: Article

References (43)

1. Altman D (1991) Practical statistics for medical research. Chapman and Hall, London
2. Buckeridge DL, Jauvin C, Okhmatovskaia A, Verma AD (2011) Simulation Analysis Platform (SnAP): a tool for evaluation of public health surveillance and disease control strategies. AMIA Annu Symp Proc 2011:161–170
3. Castiglione F, Pappalardo F, Bernaschi M, Motta S (2007) Optimization of HAART with genetic algorithms and agent-based models of HIV infection. Bioinformatics 23(24):3350–3355
4. Coello C (2013) List of references on evolutionary multiobjective optimization. http://www.lania.mx/ccoello/EMOO/EMOObib.html
5. Cohen J (1960) A coefficient of agreement for nominal scales. Educ Psychol Meas 20(1):37–46
6. Cohen J (1968) Weighted kappa: nominal scale agreement with provision for scaled disagreement or partial credit. Psychol Bull 70(4):213–220
7. Collins C, Lenhart S, Nanda S, Xiong J, Yakovlev K, Yong J (2012) Optimal control of harvesting in a stochastic metapopulation model. Optim Control Appl Methods 33(2):127–142
8. Ding W, Gross LJ, Langston K, Lenhart S, Real LA (2007) Rabies in raccoons: optimal control for a discrete time model on a spatial grid. J Biol Dyn 1(4):379–393
9. Edwards M, Huet S, Goreaud F, Deffuant G (2003) Comparing an individual-based model of behavior diffusion with its mean field aggregate approximation. J Artif Soc Soc Simul 6(4)
10. Eugenio BD (2000) On the usage of kappa to evaluate agreement on coding tasks. In: Proceedings of the Second International Conference on Language Resources and Evaluation, pp 441–444
11. Fleiss JL (1971) Measuring nominal scale agreement among many raters. Psychol Bull 76(5):378–382
12. Gani J, Yakowitz S (1995) Error bounds for deterministic approximations to Markov processes, with applications to epidemic models. J Appl Probab 32(4):1063–1076
13. Gennert MA, Yuille A (1988) Determining the optimal weights in multiple objective function optimization. In: Computer Vision., Second International Conference on, pp 87–89
14. Goldberg D (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading
15. Grimm V, Berger U, DeAngelis DL, Polhill JG, Giske J, Railsback SF (2010) The ODD protocol: a review and first update. Ecol Model 221(23):2760–2768
16. Hayek N (2011) Infinite horizon multiobjective optimal control problems in the discrete time case. Optimization 60(4):509–529
17. Hinkelmann F, Murrugarra D, Jarrah A, Laubenbacher R (2011) A mathematical framework for agent based models of complex biological networks. Bull Math Biol 73(7):1583–1602
18. Horn J, Nafpliotis N, Goldberg D (1994) A niched Pareto genetic algorithm for multiobjective optimization. In: Evolutionary Computation, 1994, vol. 1. IEEE World Congress on Computational Intelligence., Proceedings of the First IEEE Conference on., pp 82–87
19. Huet S, Edwards M, Deffuant G (2007) Taking into account the variations of neighbourhood sizes in the mean-field approximation of the threshold model on a random network. J Artif Soc Soc Simul 10(1)
20. Hwang CL, Fan LT (1967) A discrete version of Pontryagin’s maximum principle. Oper Res 15(1):139–146
21. Jacquez JA, Simon CP (1993) The stochastic SI model with recruitment and deaths I. Comparison with the closed SIS model. Math Biosci 117(1–2):77–125
22. Kasaie P, Kelton W, Vaghefi A, Naini S (2010) Toward optimal resource-allocation for control of epidemics: an agent-based-simulation approach. In: Winter Simulation Conference (WSC), Proceedings of the 2010, pp 2237–2248
23. Kim PS, Lee PP, Levy D (2008a) A PDE model for imatinib-treated chronic myelogenous leukemia. Bull Math Biol 70:1994–2016
24. Kim PS, Lee PP, Levy D (2008b) Modeling imatinib-treated chronic myelogenous leukemia: reducing the complexity of agent-based models. Bull Math Biol 70:728–744
25. Krippendorff K (1980) Content analysis: an introduction to its methodology. Sage Publications, Beverly Hills
26. Laubenbacher R, Jarrah AS, Mortveit H, Ravi SS (2009) Mathematical formalism for agent-based modeling. In: Meyers R (ed) Encyclopedia of complexity and systems science. Springer, Berlin, pp 160–176
27. Laubenbacher R, Hinkelmann F, Oremland M (2013) Agent-based models and optimal control in biology: a discrete approach. In: Robeva R, Hodge TL (eds) Mathematical concepts and methods in modern biology. Academic Press, Boston, pp 143–178
28. Lenhart S, Workman J (2007) Optimal control applied to biological models. Chapman and Hall/CRC, Boca Raton
29. Lollini PL, Motta S, Pappalardo F (2006) Discovery of cancer vaccination protocols with a genetic algorithm driving an agent based simulator. BMC Bioinform 7:352
30. Lugo CA, McKane AJ (2008) Quasicycles in a spatial predator-prey model. Phys Rev E 78(051):911
31. Mao L (2011) Agent-based simulation for weekend-extension strategies to mitigate influenza outbreaks. BMC Public Health 11:522
32. MATLAB (2014) version 8.3.0 (R2014a). The MathWorks, Inc., Natick, MA
33. Matsuda H, Ogita N, Sasaki A, Satō K (1992) Statistical mechanics of population. Prog Theor Phys 88(6):1035–1049
34. Moore H (1897) Cours d’economie politique. by vilfredo pareto, professeur l’universite de lausanne. vol. i. pp. 430. i896. vol. ii. pp. 426. i897. lausanne: F. rouge. The ANNALS of the American Academy of Political and Social Science 9(3):128–131
35. Okell LC, Drakeley CJ, Bousema T, Whitty CJ, Ghani AC (2008) Modelling the impact of artemisinin combination therapy and long-acting treatments on malaria transmission intensity. PLoS Med 5:e226 Discussion
36. Ovaskainen O, Cornell SJ (2006) Space and stochasticity in population dynamics. Proc Natl Acad Sci USA 103(34):12,781–12,786
37. Parunak H, Savit R, Riolo RL (1998) Agent-based modeling vs. equation-based modeling: A case study and users guide. In: Sichman JS, Conte R, Gilbert N (eds) Multi-agent systems and agent-based simulation, vol 1534., Lecture Notes in Computer ScienceSpringer, Berlin, pp 10–25
38. Patel R, Longini IM Jr, Halloran ME (2005) Finding optimal vaccination strategies for pandemic influenza using genetic algorithms. J Theor Biol 234(2):201–212
39. Pennisi M, Catanuto R, Pappalardo F, Motta S (2008) Optimal vaccination schedules using simulated annealing. Bioinformatics 24:1740–1742
40. Rahmandad H, Sterman J (2008) Heterogeneity and network structure in the dynamics of diffusion: comparing agent-based and differential equation models. Manag Sci 54(5):998–1014
41. Wilensky U (2009) Netlogo. Center for connected learning and computer-based modeling, Northwestern University, Evanston, http://ccl.northwestern.edu/netlogo/
42. Wilson WG (1998) Resolving discrepancies between deterministic population models and individual-based simulations. Am Nat 151(2):116–134
43. Yang Y, Atkinson PM, Ettema D (2011) Analysis of CDC social control measures using an agent-based simulation of an influenza epidemic in a city. BMC Infect Dis 11:199