Robust viability analysis of a controlled epidemiological model
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 u...
- Autores:
-
Sepúlveda Salcedo, Lilian Sofía
De Lara, Michel
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2019
- Institución:
- Universidad Autónoma de Occidente
- Repositorio:
- RED: Repositorio Educativo Digital UAO
- Idioma:
- eng
- OAI Identifier:
- oai:red.uao.edu.co:10614/11519
- Palabra clave:
- Control vectorial
Vector control
Epidemics control
Viability
Uncertainty and robustness
Ross–Macdonald model
Dengue
- Rights
- openAccess
- License
- Derechos Reservados - Universidad Autónoma de Occidente
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Robust viability analysis of a controlled epidemiological model |
| title |
Robust viability analysis of a controlled epidemiological model |
| spellingShingle |
Robust viability analysis of a controlled epidemiological model Control vectorial Vector control Epidemics control Viability Uncertainty and robustness Ross–Macdonald model Dengue |
| title_short |
Robust viability analysis of a controlled epidemiological model |
| title_full |
Robust viability analysis of a controlled epidemiological model |
| title_fullStr |
Robust viability analysis of a controlled epidemiological model |
| title_full_unstemmed |
Robust viability analysis of a controlled epidemiological model |
| title_sort |
Robust viability analysis of a controlled epidemiological model |
| dc.creator.fl_str_mv |
Sepúlveda Salcedo, Lilian Sofía De Lara, Michel |
| dc.contributor.author.none.fl_str_mv |
Sepúlveda Salcedo, Lilian Sofía De Lara, Michel |
| dc.subject.armarc.spa.fl_str_mv |
Control vectorial |
| topic |
Control vectorial Vector control Epidemics control Viability Uncertainty and robustness Ross–Macdonald model Dengue |
| dc.subject.armarc.eng.fl_str_mv |
Vector control |
| dc.subject.proposal.eng.fl_str_mv |
Epidemics control Viability Uncertainty and robustness Ross–Macdonald model Dengue |
| description |
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 |
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2019 |
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2019-11-15T20:37:10Z |
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2019-11-15T20:37:10Z |
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2019-04 |
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58 |
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126 |
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Sepúlveda Salcedo, L. S., & De Lara, M. (2019). Robust viability analysis of a controlled epidemiological model. Theoretical population biology, 126, 51-58. https://doi.org/10.1016/j.tpb.2019.02.003 |
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Theoretical Population Biology |
| dc.relation.references.none.fl_str_mv |
Anderson and May, 1992 Anderson R.M., May R.M. Infectious Diseases of Humans: Dynamics and Control Oxford Science Publications, OUP Oxford (1992) Aubin, 1991 Aubin J. Viability theory Systems & Control: Foundations & Applications, Birkhäuser Boston Inc., Boston, MA (1991) Béné and Doyen, 2008 Béné C., Doyen L. Contribution values of biodiversity to ecosystem performances: a viability perspective Ecol. Econom., 68 (1–2) (2008), pp. 14-23 Béné et al., 2001 Béné C., Doyen L., Gabay D. A viability analysis for a bio-economic model Ecol. Econom., 36 (2001), pp. 385-396 Bonneuil and Müllers, 1997 Bonneuil N., Müllers K. Viable populations in a prey-predator system J. Math. Biol., 35 (3) (1997), pp. 261-293 Bonneuil and Saint-Pierre, 2005 Bonneuil N., Saint-Pierre P. Population viability in three trophic-level food chains Appl. Math. Comput., 169 (2) (2005), pp. 1086-1105 Brauer and Castillo-Chávez, 2001 Brauer F., Castillo-Chávez C. Mathematical models in population biology and epidemiology Texts in Applied Mathematics, Vol. 40, Springer-Verlag, New York (2001) Costero et al., 1998 Costero A., Edman J.D., Clark G.G., Scott T.W. Life table study of Aedes aegypti (diptera: Culicidae) in Thailand and Puerto Rico fed only human blood plus sugar J. Med. Entomol., 35 (5) (1998) De Lara and Doyen, 2008 De Lara M., Doyen L. Sustainable Management of Natural Resources, Mathematical Models and Methods, Springer-Verlag, Berlin (2008) De Lara and Sepulveda, 2016 De Lara M., Sepulveda L. Viable control of an epidemiological model Math. Biosci., 280 (2016), pp. 24-37 Diekmann and Heesterbeek, 2000 Diekmann O., Heesterbeek J.A.P. Mathematical Epidemiology of Infectious Diseases Wiley, Utrecht, Netherland (2000) Hethcote, 2000 Hethcote H.W. The mathematics of infectious diseases SIAM Rev., 42 (2000), pp. 599-653 Jansen and Beebe, 2010 Jansen C.C., Beebe N.W. The dengue vector aedes aegypti: what comes next Microbes Infect., 12 (4) (2010), pp. 272-279 Méndez et al., 2006 Méndez F., Barreto M., Arias J., Rengifo G., Muñoz J., Burbano M., Parra B. Human and mosquito infections by dengue viruses during and after epidemics in a dengue-endemic region of Colombia Am. J. Trop. Med. Hyg., 74 (4) (2006), pp. 678-683 Moré, 1977 Moré J.J. The Levenberg–Marquardt algorithm: implementation and theory Watson G.A. (Ed.), Numerical Analysis: Proceedings of the Biennial Conference Held at Dundee, Springer Berlin Heidelberg, Berlin, Heidelberg (1977), pp. 105-116 Regnier and De Lara, 2015 Regnier E., De Lara M. Robust viable analysis of a harvested ecosystem model Environ. Modeling & Assess., 20 (6) (2015), pp. 687-698 Scott et al., 2000ª Scott T.W., Amerasinghe P.H., Morrison A.C., Lorenz L.H., Clark G.G., Strickman D., Kittayapong P., Edman J.D. Longitudinal studies of Aedes aegypti (diptera: Culicidae) in Thailand and Puerto Rico: blood feeding frequency J. Med. Entomol., 37 (1) (2000), p. 89 Scott et al., 2000b Scott T.W., Morrison A.C., Lorenz L.H., Clark G.G., Strickman D., Kittayapong P., Zhou H., Edman J.D. Longitudinal studies of Aedes aegypti (diptera: Culicidae) in Thailand and Puerto Rico: population dynamics J. Med. Entomol., 37 (1) (2000), p. 77 Smith et al., 2007 Smith D.L., McKenzie F.E., Snow R.W., Hay S.I. Revisiting the basic reproductive number for malaria and its implications for malaria control PLoS Biol., 5 (3) (2007), Article e4202 |
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Sepúlveda Salcedo, Lilian Sofíavirtual::4681-1De Lara, Michel8db5d31c72945b494e63a6160c82b9f2Universidad Autónoma de Occidente. Calle 25 115-85. Km 2 vía Cali-Jamundí2019-11-15T20:37:10Z2019-11-15T20:37:10Z2019-04405809http://hdl.handle.net/10614/11519https://doi.org/10.1016/j.tpb.2019.02.003Managing 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 controlapplication/pdf8 páginasengElsevierDerechos Reservados - Universidad Autónoma de Occidentehttps://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)http://purl.org/coar/access_right/c_abf2instname:Universidad Autónoma de Occidentereponame:Repositorio Institucional UAORobust viability analysis of a controlled epidemiological modelArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTREFinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85Control vectorialVector controlEpidemics controlViabilityUncertainty and robustnessRoss–Macdonald modelDengue5851126Sepúlveda Salcedo, L. S., & De Lara, M. (2019). Robust viability analysis of a controlled epidemiological model. Theoretical population biology, 126, 51-58. https://doi.org/10.1016/j.tpb.2019.02.003Theoretical Population BiologyAnderson and May, 1992 Anderson R.M., May R.M. Infectious Diseases of Humans: Dynamics and Control Oxford Science Publications, OUP Oxford (1992)Aubin, 1991 Aubin J. Viability theory Systems & Control: Foundations & Applications, Birkhäuser Boston Inc., Boston, MA (1991)Béné and Doyen, 2008 Béné C., Doyen L. Contribution values of biodiversity to ecosystem performances: a viability perspective Ecol. Econom., 68 (1–2) (2008), pp. 14-23Béné et al., 2001 Béné C., Doyen L., Gabay D. A viability analysis for a bio-economic model Ecol. Econom., 36 (2001), pp. 385-396Bonneuil and Müllers, 1997 Bonneuil N., Müllers K. Viable populations in a prey-predator system J. Math. Biol., 35 (3) (1997), pp. 261-293Bonneuil and Saint-Pierre, 2005 Bonneuil N., Saint-Pierre P. Population viability in three trophic-level food chains Appl. Math. Comput., 169 (2) (2005), pp. 1086-1105Brauer and Castillo-Chávez, 2001 Brauer F., Castillo-Chávez C. Mathematical models in population biology and epidemiology Texts in Applied Mathematics, Vol. 40, Springer-Verlag, New York (2001)Costero et al., 1998 Costero A., Edman J.D., Clark G.G., Scott T.W. Life table study of Aedes aegypti (diptera: Culicidae) in Thailand and Puerto Rico fed only human blood plus sugar J. Med. Entomol., 35 (5) (1998)De Lara and Doyen, 2008 De Lara M., Doyen L. Sustainable Management of Natural Resources, Mathematical Models and Methods, Springer-Verlag, Berlin (2008)De Lara and Sepulveda, 2016 De Lara M., Sepulveda L. Viable control of an epidemiological model Math. Biosci., 280 (2016), pp. 24-37Diekmann and Heesterbeek, 2000 Diekmann O., Heesterbeek J.A.P. Mathematical Epidemiology of Infectious Diseases Wiley, Utrecht, Netherland (2000)Hethcote, 2000 Hethcote H.W. The mathematics of infectious diseases SIAM Rev., 42 (2000), pp. 599-653Jansen and Beebe, 2010 Jansen C.C., Beebe N.W. The dengue vector aedes aegypti: what comes next Microbes Infect., 12 (4) (2010), pp. 272-279Méndez et al., 2006 Méndez F., Barreto M., Arias J., Rengifo G., Muñoz J., Burbano M., Parra B. Human and mosquito infections by dengue viruses during and after epidemics in a dengue-endemic region of Colombia Am. J. Trop. Med. Hyg., 74 (4) (2006), pp. 678-683Moré, 1977 Moré J.J. The Levenberg–Marquardt algorithm: implementation and theory Watson G.A. (Ed.), Numerical Analysis: Proceedings of the Biennial Conference Held at Dundee, Springer Berlin Heidelberg, Berlin, Heidelberg (1977), pp. 105-116Regnier and De Lara, 2015 Regnier E., De Lara M. Robust viable analysis of a harvested ecosystem model Environ. Modeling & Assess., 20 (6) (2015), pp. 687-698Scott et al., 2000ª Scott T.W., Amerasinghe P.H., Morrison A.C., Lorenz L.H., Clark G.G., Strickman D., Kittayapong P., Edman J.D. Longitudinal studies of Aedes aegypti (diptera: Culicidae) in Thailand and Puerto Rico: blood feeding frequency J. Med. Entomol., 37 (1) (2000), p. 89Scott et al., 2000b Scott T.W., Morrison A.C., Lorenz L.H., Clark G.G., Strickman D., Kittayapong P., Zhou H., Edman J.D. Longitudinal studies of Aedes aegypti (diptera: Culicidae) in Thailand and Puerto Rico: population dynamics J. Med. Entomol., 37 (1) (2000), p. 77Smith et al., 2007 Smith D.L., McKenzie F.E., Snow R.W., Hay S.I. 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