Numerical Optimization Identification of a Keller-Segel Model for Thermoregulation in Honey Bee Colonies in Winter

1. Alifanov, O.M., Artioukhine, E.A., Rumyantsev, S.V.: Extreme Methods for Solving Ill-posed problems with Applications to Inverse Heat Transfer Problems. Begell House, New York (1995)

   MATH  Google Scholar 

2. Atanasov, A.Z., Koleva, M.N., Vulkov, L.G.: Numerical analysis of thermoregulation in honey bee colonies in winter based on sign-changing chemotactic coefficient model. In: Springer Proceedings in Mathematics and Statistics, submitted, July 2022

   Google Scholar 

3. Atanasov, A.Z., Georgiev, S.G., Vulkov, L.G.: Reconstruction analysis of honeybee colony collapse disorder modeling. Optim. Eng. 22(4), 2481–2503 (2021). https://doi.org/10.1007/s11081-021-09678-0

   Article  MathSciNet  MATH  Google Scholar 

4. Bagheri, S., Mirzaie, M.: A mathematical model of honey bee colony dynamics to predict the effect of pollen on colony failure. PLoS ONE 14(11), e0225632 (2019)

   Article  Google Scholar 

5. Bakhvalov, N.S.: Numerical Methods, p. 663. Mir Publishers, Moscow (1977). Translated from Russian to English

   Google Scholar 

6. Bastaansen, R., Doelman, A., van Langevede, F., Rottschafer, V.: Modeling honey bee colonies in winter using a Keller-Segel model with a sign-changing chemotactic coefficient. SIAM J. Appl. Math. 80(20), 839–863 (2020)

   Article  MathSciNet  MATH  Google Scholar 

7. Bellomo, N., Bellouquid, A., Tao, Y., Winkler, M.: Toward a mathematical theory of Keller-Segel models of patern formulation in biological tissues. Math. Models Methods Appl. Sci. 25(09), 1663–1763 (2015)

   Article  MathSciNet  MATH  Google Scholar 

8. Calovi, M., Grozinger, C.M., Miller, D.A., Goslee, S.C.: Summer weather conditions influence winter survival of honey bees (Apis mellifera) in the northeastern United States. Sci. Rep. 11, 1553 (2021)

   Article  Google Scholar 

9. Cao, K., Lesnic, D.: Reconstruction of the perfusion coefficient from temperature measurements using the conjugate gradient method. Int. J. Comput. Math. 95(4), 797–814 (2018)

   Article  MathSciNet  MATH  Google Scholar 

10. Chavent, G.: Nonlinear Least Squares for Inverse Problems: Theoretical Foundation and Step-by Guide for Applications. Springer, Cham (2009)

    MATH  Google Scholar 

11. Chen, J., DeGrandi-Hoffman, G., Ratti, V., Kang, Y.: Review on mathematical modeling of honeybee population dynamics. Math. Biosci. Eng. 18(6), 9606–9650 (2021)

    Article  MathSciNet  MATH  Google Scholar 

12. Esch, H.: Über die körpertemperaturen und den wärmehaushalt von Apis mellifica. Z. Vergleich. Physiol. 43, 305–335 (1960). https://doi.org/10.1007/BF00298066

    Article  Google Scholar 

13. Fakhraie, M., Shidfar, A., Garshasbi, M.: A computational procedure for estimation of an unknown coefficient in an inverse boundary value problem. Appl. Math. Comput. 187, 1120–1125 (2007)

    MathSciNet  MATH  Google Scholar 

14. Guzman-Novoa, E., Eccles, C.Y., McGowan, J., Kelly, P.G., Correa- Bentez, A.: Varroa destructor is the main culprit for the death and reduced populations of overwintered honey bee (Apis mellifera) colonies in Ontario, Canada. Apidologie 41, 443–450 (2010)

    Article  Google Scholar 

15. Hanke, M.: Conjugate Gradient Type Methods for Ill-Posed Problems, p. 144. Chapman and Hall/CRC, NewYork (1995)

    MATH  Google Scholar 

16. Hasanov, A., Romanov, V.: Introduction to the Inverse Problems for Differential Equations. Springer, NewYork (2017). https://doi.org/10.1007/978-3-319-62797-7

    Book  MATH  Google Scholar 

17. Heinrich, B.: Energetics of honeybee swarm thermoregulation. Science 212, 565–566 (1981)

    Article  Google Scholar 

18. Kevan, P.G., Guzman, E., Skinner A., van Engelsdorp, D.: Colony collapse disorder in Canada: do we have a problem? HiveLights, pp. 14–16, May (2007). http://hdl.handle.net/10214/2418

19. Krivorotko, O., Kabanikhin, S., Zhang, S., Kashtanova, V.: Global and local optimization in identification of parabolic systems. J. Inverse Ill-Posed Prob. 28(6), 899–913 (2020)

    Article  MathSciNet  MATH  Google Scholar 

20. Lemke, M., Lamprecht, A.: A model of heat production and thermoregulation in winter clusters of honey bee using differential heat conduction equations. J. Theor. Biol. 142(2), 261–273 (1990)

    Article  Google Scholar 

21. Lesnic, D.: Inverse Problems with Applications in Science and Engineering. CRC Press, London (2020)

    MATH  Google Scholar 

22. Ocko, S.A., Mahadevan, L.: Collective thermoregulation in bee clusters. J. R. Soc. Interface 11(91), 20131033 (2014)

    Article  Google Scholar 

23. Samarskii, A.A.: The Theory of Difference Schemes. Marcel Dekker Inc, New York (2001)

    Book  MATH  Google Scholar 

24. Peters, J.M., Peleg, O., Mahadevan, L.: Collective ventilation in honeybee nest. J. R. Soc. Interface 16(150), 20180561 (2019)

    Article  Google Scholar 

25. Ratti, V., Kevan, P.G., Eberl, H.J.: A mathematical model of forager loss in honeybee colonies infested with varroa destructor and the acute bee paralysis virus. Bull. Math. Biol. 79(6), 1218–1253 (2017). https://doi.org/10.1007/s11538-017-0281-6

    Article  MathSciNet  MATH  Google Scholar 

26. Stabentheiner, A., Kovac, H., Brodschneider, R.: Honeybee colony thermoregulation regulatory mechanisms and contribution of individuals in dependence on age, location and thermal stress. PLoS ONE 5(1), e8967 (2010)

    Article  Google Scholar 

27. Tautz, J.: The Buzz about Bees: Biology of a Superorganism. Springer, Berlin (2008). https://doi.org/10.1007/978-3-540-78729-7

    Book  Google Scholar 

28. Wang, B., Liu, J.: Recovery of thermal conductivity in two-dimensional media with nonlinear source by optimizations. Appl. Math. Lett. 60, 73–80 (2016)

    Article  MathSciNet  MATH  Google Scholar 

29. Watmough, J., Camazine, S.: Self-organized thermoregulation of honeybee clusters. J. Theor. Biol. 176(3), 391–402 (1995)

    Article  Google Scholar 

Download references