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Optimal Disease Eradication in Sympatric Metapopulations

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Abstract

The paper analyses the management of an infectious disease in a sympatric metapopulation, under both Nash and cooperative behaviour, through the development of a differential game and an optimal control problem with connected local state variables. As pathogens are renewable resources with negative value, the problem may be non-convex. Since the disease can be transmitted across various connected populations, externalities may be involved. A numerical application is presented, with reference to a livestock disease that can be transmitted between herds on common pastures. The results suggest that optimal eradication in finite time should be pursued when possible. However, optimal eradication is not always feasible (sometimes eradication can be only achieved asymptotically), and the ecology of the disease is of paramount importance in this respect. Also, convergence to an internal steady-state does not minimise the present value of the disease damage and control cost (a result consistent with the existing literature). Ignoring these results may lead to inadequate policy design.

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Authors and Affiliations

  1. Department of Public Governance, MODUL University Vienna, Am Kahlenberg 1, 1190, Vienna, Austria

    M. G. Ceddia

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  1. M. G. Ceddia
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Correspondence to M. G. Ceddia.

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Ceddia, M.G. Optimal Disease Eradication in Sympatric Metapopulations. Environ Resource Econ 52, 499–530 (2012). https://doi.org/10.1007/s10640-011-9540-4

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