General Idea: Model the invader dynamics + optimization of invasion/control costs (integrative bioeconomic models) Population level Dispersal IntroductionTransportation Prevention/ Control Costs Optimization Expenses Losses

Population level Dispersal Introdu ction Transporta tion Prevention/ Control Costs Optimization Expens es Lo sse s Optimal control Work done: macroscopic lake system invasion model, description in terms of % lakes invaded, mean costs and losses. Generalization: invader eradication. Technical issues - OCT may have several locally-optimal solutions. Globally optimal – switches between them. “Management catastrophes”: small change in data – big change in management policy. Simplified/ averaged Optimal control

Macroscopic model with eradication only: Multiple locally-optimal OC solutions No control Partial eradication Complete eradication Initial invasion level Desired time horizon (one of the lines)

N-lakes model B ij invaded

Basic N-lake Problems a)Optimal invasion stopping – how to choose controls to make all flows <W 0 ? Optimal stopping configurations, maybe optimal retreat. b)Optimal control. Uniquiness? Easy to solve, hard to guarantee global optimality. c)[future] Apply SDP? Guarantees global optimality. Complexity reduction – pseudo states (neural networks). d)NN - problem-dependent technique, so what is the best problem to apply?