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Robust viability analysis of a controlled epidemiological model

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  • 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
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    References listed on IDEAS

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    1. Esther Regnier & Michel de Lara, 2015. "Robust Viable Analysis of a Harvested Ecosystem Model," Post-Print hal-03261529, HAL.
    2. Esther Regnier & Michel de Lara, 2015. "Robust Viable Analysis of an Ecosystem Model," PSE-Ecole d'économie de Paris (Postprint) halshs-00786409, HAL.
    3. Esther Regnier & Michel de Lara, 2015. "Robust Viable Analysis of a Harvested Ecosystem Model," PSE-Ecole d'économie de Paris (Postprint) hal-03261529, HAL.
    4. 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.
    5. 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.
    6. 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.
    Full references (including those not matched with items on IDEAS)

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