IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v126y2019icp51-58.html
   My bibliography  Save this article

Robust viability analysis of a controlled epidemiological model

Author

Listed:
  • Sepulveda Salcedo, Lilian Sofia
  • De Lara, Michel

Abstract

Managing infectious diseases is a world public health issue, plagued by uncertainties. In this paper, we analyze the problem of viable control of a dengue outbreak under uncertainty. For this purpose, we develop a controlled Ross–Macdonald model with mosquito vector control by fumigation, and with uncertainties affecting the dynamics; both controls and uncertainties are supposed to change only once a day, then remain stationary during the day. The robust viability kernel is the set of all initial states such that there exists at least a strategy of insecticide spraying which guarantees that the number of infected individuals remains below a threshold, for all times, and whatever the sequences of uncertainties. Having chosen three nested subsets of uncertainties – a deterministic one (without uncertainty), a medium one and a large one – we can measure the incidence of the uncertainties on the size of the kernel, in particular on its reduction with respect to the deterministic case. The numerical results show that the viability kernel without uncertainties is highly sensitive to the variability of parameters — here the biting rate, the probability of infection to mosquitoes and humans, and the proportion of female mosquitoes per person. So, a robust viability analysis is a possible tool to reveal the importance of uncertainties regarding epidemics control.

Suggested Citation

  • Sepulveda Salcedo, Lilian Sofia & De Lara, Michel, 2019. "Robust viability analysis of a controlled epidemiological model," Theoretical Population Biology, Elsevier, vol. 126(C), pages 51-58.
    • Handle: RePEc:eee:thpobi:v:126:y:2019:i:c:p:51-58
    DOI: 10.1016/j.tpb.2019.02.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580917301430
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tpb.2019.02.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Esther Regnier & Michel de Lara, 2015. "Robust Viable Analysis of a Harvested Ecosystem Model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03261529, HAL.
    2. Esther Regnier & Michel de Lara, 2015. "Robust Viable Analysis of a Harvested Ecosystem Model," Post-Print hal-03261529, HAL.
    3. Esther Regnier & Michel de Lara, 2015. "Robust Viable Analysis of an Ecosystem Model," PSE-Ecole d'économie de Paris (Postprint) halshs-00786409, HAL.
    4. Esther Regnier & Michel de Lara, 2015. "Robust Viable Analysis of a Harvested Ecosystem Model," PSE-Ecole d'économie de Paris (Postprint) hal-03261529, HAL.
    5. Bene, C. & Doyen, L. & Gabay, D., 2001. "A viability analysis for a bio-economic model," Ecological Economics, Elsevier, vol. 36(3), pages 385-396, March.
    6. Béné, C. & Doyen, L., 2008. "Contribution values of biodiversity to ecosystem performances: A viability perspective," Ecological Economics, Elsevier, vol. 68(1-2), pages 14-23, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jean-Christophe Pereau & Lauriane Mouysset & Luc Doyen, 2018. "Groundwater Management in a Food Security Context," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 71(2), pages 319-336, October.
    2. Doyen, Luc & Péreau, Jean-Christophe, 2012. "Sustainable coalitions in the commons," Mathematical Social Sciences, Elsevier, vol. 63(1), pages 57-64.
    3. Michel De Lara & Vincent Martinet & Luc Doyen, 2010. "Risk and Sustainability : Is Viability that far from Optimality?," EconomiX Working Papers 2010-7, University of Paris Nanterre, EconomiX.
    4. A.A. Cisse & L. Doyen & F. Blanchard & J.C. Pereau, 2013. "Stochastic viability of the coastal fishery in French Guiana," Documents de Travail 2013-07, CEREGMIA, Université des Antilles et de la Guyane.
    5. Coralie KERSULEC & Luc DOYEN, 2022. "From fork to fish: The role of consumer preferences on the sustainability of fisheries," Bordeaux Economics Working Papers 2022-10, Bordeaux School of Economics (BSE).
    6. Doyen, L. & Thébaud, O. & Béné, C. & Martinet, V. & Gourguet, S. & Bertignac, M. & Fifas, S. & Blanchard, F., 2012. "A stochastic viability approach to ecosystem-based fisheries management," Ecological Economics, Elsevier, vol. 75(C), pages 32-42.
    7. Michel de Lara & Vincent Martinet & Luc Doyen, 2015. "Satisficing versus optimality: criteria for sustainability," Post-Print hal-01123050, HAL.
    8. Doyen, L. & Armstrong, C. & Baumgärtner, S. & Béné, C. & Blanchard, F. & Cissé, A.A. & Cooper, R. & Dutra, L.X.C. & Eide, A. & Freitas, D. & Gourguet, S. & Gusmao, F. & Hardy, P.-Y. & Jarre, A. & Litt, 2019. "From no whinge scenarios to viability tree," Ecological Economics, Elsevier, vol. 163(C), pages 183-188.
    9. Baumgärtner, Stefan & Quaas, Martin F., 2009. "Ecological-economic viability as a criterion of strong sustainability under uncertainty," Ecological Economics, Elsevier, vol. 68(7), pages 2008-2020, May.
    10. Jollands, Nigel & Harmsworth, Garth, 2007. "Participation of indigenous groups in sustainable development monitoring: Rationale and examples from New Zealand," Ecological Economics, Elsevier, vol. 62(3-4), pages 716-726, May.
    11. Chapel, Laetitia & Deffuant, Guillaume & Martin, Sophie & Mullon, Christian, 2008. "Defining yield policies in a viability approach," Ecological Modelling, Elsevier, vol. 212(1), pages 10-15.
    12. Esther Regnier & Michel de Lara, 2014. "Robust Viable Analysis of an Ecosystem Model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00786409, HAL.
    13. repec:dav:journl:y:2016:v:7:i:11:p:1272-1289 is not listed on IDEAS
    14. Martin F. Quaas & Ralph Winkler, 2017. "A Market Mechanism for Sustainable and Efficient Resource Use under Uncertainty," CESifo Working Paper Series 6524, CESifo.
    15. Cissé, A.A. & Gourguet, S. & Doyen, L. & Blanchard, F. & Péreau, J.-C., 2013. "A bio-economic model for the ecosystem-based management of the coastal fishery in French Guiana," Environment and Development Economics, Cambridge University Press, vol. 18(3), pages 245-269, June.
    16. Krawczyk, Jacek B & Pharo, Alastair S, 2014. "Manual of VIKAASA 2.0: An application for computing and graphing viability kernels for simple viability problems," Working Paper Series 3432, Victoria University of Wellington, School of Economics and Finance.
    17. V.Martinet & L. Doyen, 2003. "Sustainable management of an exhaustible resource:a viable control model," THEMA Working Papers 2003-36, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    18. Doyen, L. & Martinet, V., 2012. "Maximin, viability and sustainability," Journal of Economic Dynamics and Control, Elsevier, vol. 36(9), pages 1414-1430.
    19. Krawczyk, Jacek B & Pharo, Alastair S, 2011. "Manual of VIKAASA: An application capable of computing and graphing viability kernels for simple viability problems," Working Paper Series 1878, Victoria University of Wellington, School of Economics and Finance.
    20. Antoine Brias & Jean-Denis Mathias & Guillaume Deffuant, 2016. "Accelerating viability kernel computation with CUDA architecture: application to bycatch fishery management," Computational Management Science, Springer, vol. 13(3), pages 371-391, July.
    21. Girol Karacaoglu & Jacek B. Krawczyk, 2021. "Public policy, systemic resilience and viability theory," Metroeconomica, Wiley Blackwell, vol. 72(4), pages 826-848, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:thpobi:v:126:y:2019:i:c:p:51-58. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/intelligence .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.