Bulletin of Mathematical Biology

, Volume 79, Issue 1, pp 88–116 | Cite as

Optimal Culling and Biocontrol in a Predator–Prey Model

  • Eric NumforEmail author
  • Frank M. Hilker
  • Suzanne Lenhart
Original Article


Invasive species cause enormous problems in ecosystems around the world. Motivated by introduced feral cats that prey on bird populations and threaten to drive them extinct on remote oceanic islands, we formulate and analyze optimal control problems. Their novelty is that they involve both scalar and time-dependent controls. They represent different forms of control, namely the initial release of infected predators on the one hand and culling as well as trapping, infecting, and returning predators on the other hand. Combinations of different control methods have been proposed to complement their respective strengths in reducing predator numbers and thus protecting endangered prey. Here, we formulate and analyze an eco-epidemiological model, provide analytical results on the optimal control problem, and use a forward–backward sweep method for numerical simulations. By taking into account different ecological scenarios, initial conditions, and control durations, our model allows to gain insight how the different methods interact and in which cases they could be effective.


Eco-epidemiology Biocontrol Optimal control Invasive pest Predator–prey 

Mathematics Subject Classification

34D20 49K15 92D30 92D40 



This work was partially supported by the National Institute for Mathematical and Biological Synthesis, an Institute sponsored by the National Science Foundation through NSF Award #DBI-1300426, with additional support from The University of Tennessee, Knoxville. Lenhart’s research was also partially supported by the University of Tennessee Boyd Center for Business and Economic Research.


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Copyright information

© Society for Mathematical Biology 2016

Authors and Affiliations

  • Eric Numfor
    • 1
    Email author
  • Frank M. Hilker
    • 2
  • Suzanne Lenhart
    • 3
  1. 1.Department of MathematicsAugusta UniversityAugustaUSA
  2. 2.Institute of Environmental Systems Research, School of Mathematics and Computer ScienceOsnabrück UniversityOsnabrückGermany
  3. 3.Department of MathematicsUniversity of TennesseeKnoxvilleUSA

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