Controllability with positivity constraints of the Lotka-McKendrick systemReport as inadecuate

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Abstract : This work considers the linear Lotka-McKendrick system from population dynamics with control active on individuals in a prescribed age range. The main results assert that given τ large enough but possibly smaller than the life expectancy, there exists controls driving the system to any equilibrium state or any uncontrolled trajectory in time τ. Moreover, we show that if the initial and final states are positive then the constructed controls preserve the positivity of the population density on the whole time interval 0, τ . The method is a direct one, in the spirit of some early works on the controllability of hyperbolic systems in one space dimension. Finally, we apply our method to a nonlinear infection-age model.

Keywords : Controllability Population dynamics Positivity

Author: Nicolas Hegoburu - Pierre Magal - Marius Tucsnak -



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