Figure 1.
Flow diagram showing infection within, and transfer between, hospital and community compartments. Rates are per capita
-
Previous Article
Dynamics of a stochastic delayed Harrison-type predation model: Effects of delay and stochastic components
- MBE Home
- This Issue
-
Next Article
Early and late stage profiles for a chemotaxis model with density-dependent jump probability
December
2018, 15(6): 1387-1399.
doi: 10.3934/mbe.2018063
Ebola: Impact of hospital's admission policy in an overwhelmed scenario
Deaprtment of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, USA |
Infectious disease outbreaks sometimes overwhelm healthcare facilities. A recent case occurred in West Africa in 2014 when an Ebola virus outbreak overwhelmed facilities in Sierra Leone, Guinea and Liberia. In such scenarios, how many patients can hospitals admit to minimize disease burden? This study considers what type of hospital admission policy during a hypothetical Ebola outbreak can better serve the community, if overcrowding degrades the hospital setting. Our result shows that which policy minimizes loss to the community depends on the initial estimation of the control reproduction number, $R_0$. When the outbreak grows extremely fast ($R_0$$ \gg $1) it is better (in terms of total disease burden) to stop admitting patients after reaching the carrying capacity because overcrowding in the hospital makes the hospital setting ineffective at containing infection, but when the outbreak grows only a little faster than the system's ability to contain it ($R_0 \gtrsim 1$), it is better to admit patients beyond the carrying capacity because limited overcrowding still reduces infection more in the community. However, when $R_0$ is no more than a little greater than 1 (for our parameter values, 1.012), both policies result the same because the number of patients never exceeds the maximum capacity.
Keywords:
Overcrowded hospital,
Ebola,
admission policy,
mathematical model,
overwhelmed healthcare facility,
control reproduction number,
basic reproduction number.
Mathematics Subject Classification:
92D30.
Citation:
Mondal Hasan Zahid, Christopher M. Kribs. Ebola: Impact of hospital's admission policy in an overwhelmed scenario. Mathematical Biosciences & Engineering,
2018, 15
(6)
: 1387-1399.
doi: 10.3934/mbe.2018063
![]()
References:
| [1] |
Central Intelligence Agency, CIA. The World Factbook, Update date: 03-01-2016, https://www.cia.gov/library/publications/the-world-factbook/fields/2227.html, Access date: 03-07-2017. Google Scholar |
| [2] |
M. D. Ahmad, M. Usman, A. Khan and M. Imran, Control analysis of Ebola disease with control strategies of quarantine and vaccination,
Infectious Disease of Poverty, 5 (2016), 72.
doi: 10.1186/s40249-016-0161-6. |
| [3] |
M. Ajelli, S. Parlamento1, D. Bome, A. Kebbi, A. Atzori, C. Frasson, G. Putoto, D. Carraro and S. Merler, The 2014 Ebola virus disease outbreak in Pujehun, Sierra Leone: epidemiology and impact of interventions,
BMC Medicine, 13 (2015), 281.
doi: 10.1186/s12916-015-0524-z. |
| [4] |
C. L. Althaus, Estimating the reproduction number of Ebola Virus (EBOV) during the 2014 outbreak in West Africa,
PLOS Currents Outbreaks, 2014.
doi: 10.1371/currents.outbreaks.91afb5e0f279e7f29e7056095255b288. |
| [5] |
R. Ansumana, K. H. Jacobsen, M. Idris, H. Bangura, M. Boie-Jalloh, J. M. Lamin, S. Sesay and F. Sahr,
Ebola in Freetown Area, Sierra Leone A case study of 581 patients, New England Journal of Medicine, 372 (2015), 587-588.
doi: 10.1056/NEJMc1413685. |
| [6] |
A. G. Buseh, P. E. Stevens, M. Bromberg and S. T. Kelber, The Ebola epidemic in West Africa: Challenges, opportunities, and policy priority areas, Nursing Outlook, 63 (2015), 30–40. http://dx.doi.org/10.1016/j.outlook.2014.12.013. Google Scholar |
| [7] |
G. Chowell, N. W. Hengartner, C. Castillo-Chavez, P. W. Fenimore and J. M. Hyman,
The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda, Journal of Theoretical Biology, 229 (2004), 119-126.
doi: 10.1016/j.jtbi.2004.03.006. |
| [8] |
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz,
On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol, 28 (1990), 365-382.
doi: 10.1007/BF00178324. |
| [9] |
J. M. Drake, R. B. Kaul, L. W. Alexander, S. M. Oegan, A. M. Kramer, J. T. Pulliam, M. J. Ferrari and A. W. Park, Ebola cases and health system demand in liberia,
PLoS Biology, 13 (2015), e1002056.
doi: 10.1371/journal.pbio.1002056. |
| [10] |
T. W. Geisbert, L. E. Hensley, P. B. Jahrling, T. Larsen, J. B. Geisbert, J. Paragas, H. A. Young, T. M. Fredeking, W. E. Rote and G. P. Vlasuk,
Treatment of Ebola virus infection with a recombinant inhibitor of factor VIIa/tissue factor: a study in rhesus monkeys, The Lancet, 362 (2003), 1953-1958.
doi: 10.1016/S0140-6736(03)15012-X. |
| [11] |
Ministry of Health, Uganda, Uganda Hospital and Health Centre IV Census Survey, 2014,198. Google Scholar |
| [12] |
P. Kazanjian, Ebola in antiquity, Clinical Infectious Disease, 61 (2015), 963-968. Google Scholar |
| [13] |
Dr. A. I. Khan, Chief Physician and Head, Hospitals, icddr, b, Dhaka, Bangladesh, Personal communication, October 11, 2017. Google Scholar |
| [14] |
Medecins Sans Frontieres, International Response to West Africa Ebola Epidemic Dangerously Inadequate, August 15, 2014. https://www.msf.org/international-response-west-africa-ebola-epidemic-dangerously-inadequate, Access date: 2018-06-01. Google Scholar |
| [15] |
Sylvie Diane Djiomba Njankou and Farai Nyabadza, Modelling the potential impact of limited hospital beds on Ebola virus disease dynamics, Mathematical Methods in the Applied Sciences, (2018), 1-17. Google Scholar |
| [16] |
World Health Organization, Ebola Situation Report, June 10, 2016. http://who.int/csr/disease/ebola/en/. Google Scholar |
| [17] |
World Health Organization, Health Statistics and Information Systems, Update date: 07-01-2016, http://www.who.int/healthinfo/global_burden_disease/metrics_daly/en/, Access date: 03-03-2017. Google Scholar |
| [18] |
World Health Organization, Liberia: Ebola Treatment Centre Sets A New Pace, October 2014. http://www.who.int/features/2014/liberia-ebola-island-clinic/en/, Access date 2018-06-01. Google Scholar |
| [19] |
World Health Organization, Why the Ebola outbreak has been underestimated, August 22, 2014. http://www.who.int/mediacentre/news/ebola/22-august-2014/en/, Access date 2018-06-01. Google Scholar |
| [20] |
E. Qin, J. Bi, M. Zhao, Y. Wang, T. Guo, T. Yan, Z. Li, J. Sun, J. Zhang, S. Chen, Y. Wu, J. Li and Y. Zhong,
Clinical features of patients with Ebola virus disease in Sierra Leone, Clinical Infectious Diseases, 61 (2015), 491-495.
doi: 10.1093/cid/civ319. |
| [21] |
J. A. Salomon, J. A. Haagsma, A. Davis, C. M. de Noordhout, S. Polinder, A. H. Havelaar, A. Cassini, B. Devleesschauwer, M. Kretzschmar, N. Speybroeck and C. J. L. Murray, Disability weights for the Global Burden of Disease 2013 study, The Lancet, 3 (2015), 712-723. Google Scholar |
| [22] |
J. S. Schieffelin, J. G. Shaffer, A. Goba, M. Gbakie, S. K. Gire, A. Colubri, R. S. G. Sealfon, L. Kanneh, A. Moigboi, M. Momoh, M. Fullah, L. M. Moses, B. L. Brown, K. G. Andersen, S. Winnicki, S. F. Schaffner, D. J. Park, N. L. Yozwiak, P.-P. Jiang, D. Kargbo, S. Jalloh, M. Fonnie, V. Sinnah, I. French, A. Kovoma, F. K. Kamara, V. Tucker, E. Konuwa, J. Sellu, I. Mustapha, M. Foday, M. Yillah, F. Kanneh, S. Saffa, J. L. B. Massally, M. L. Boisen, L. M. Branco, M. A. Vandi, D. S. Grant, C. Happi, S. M. Gevao, T. E. Fletcher, R. A. Fowler, D. G. Bausch, P. C. Sabeti, S. H. Khan and R. F. Garry,
Clinical illness and outcomes in patients with Ebola in Sierra Leone, New England Journal of Medicine, 371 (2014), 2092-2100.
doi: 10.1056/NEJMoa1411680. |
| [23] |
National Center for Health Statistics, Health, United States, 2015: With Special Feature on Racial and Ethnic Health Disparities, Hyattsville, MD. 2016. Google Scholar |
show all references
References:
| [1] |
Central Intelligence Agency, CIA. The World Factbook, Update date: 03-01-2016, https://www.cia.gov/library/publications/the-world-factbook/fields/2227.html, Access date: 03-07-2017. Google Scholar |
| [2] |
M. D. Ahmad, M. Usman, A. Khan and M. Imran, Control analysis of Ebola disease with control strategies of quarantine and vaccination,
Infectious Disease of Poverty, 5 (2016), 72.
doi: 10.1186/s40249-016-0161-6. |
| [3] |
M. Ajelli, S. Parlamento1, D. Bome, A. Kebbi, A. Atzori, C. Frasson, G. Putoto, D. Carraro and S. Merler, The 2014 Ebola virus disease outbreak in Pujehun, Sierra Leone: epidemiology and impact of interventions,
BMC Medicine, 13 (2015), 281.
doi: 10.1186/s12916-015-0524-z. |
| [4] |
C. L. Althaus, Estimating the reproduction number of Ebola Virus (EBOV) during the 2014 outbreak in West Africa,
PLOS Currents Outbreaks, 2014.
doi: 10.1371/currents.outbreaks.91afb5e0f279e7f29e7056095255b288. |
| [5] |
R. Ansumana, K. H. Jacobsen, M. Idris, H. Bangura, M. Boie-Jalloh, J. M. Lamin, S. Sesay and F. Sahr,
Ebola in Freetown Area, Sierra Leone A case study of 581 patients, New England Journal of Medicine, 372 (2015), 587-588.
doi: 10.1056/NEJMc1413685. |
| [6] |
A. G. Buseh, P. E. Stevens, M. Bromberg and S. T. Kelber, The Ebola epidemic in West Africa: Challenges, opportunities, and policy priority areas, Nursing Outlook, 63 (2015), 30–40. http://dx.doi.org/10.1016/j.outlook.2014.12.013. Google Scholar |
| [7] |
G. Chowell, N. W. Hengartner, C. Castillo-Chavez, P. W. Fenimore and J. M. Hyman,
The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda, Journal of Theoretical Biology, 229 (2004), 119-126.
doi: 10.1016/j.jtbi.2004.03.006. |
| [8] |
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz,
On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous populations, J. Math. Biol, 28 (1990), 365-382.
doi: 10.1007/BF00178324. |
| [9] |
J. M. Drake, R. B. Kaul, L. W. Alexander, S. M. Oegan, A. M. Kramer, J. T. Pulliam, M. J. Ferrari and A. W. Park, Ebola cases and health system demand in liberia,
PLoS Biology, 13 (2015), e1002056.
doi: 10.1371/journal.pbio.1002056. |
| [10] |
T. W. Geisbert, L. E. Hensley, P. B. Jahrling, T. Larsen, J. B. Geisbert, J. Paragas, H. A. Young, T. M. Fredeking, W. E. Rote and G. P. Vlasuk,
Treatment of Ebola virus infection with a recombinant inhibitor of factor VIIa/tissue factor: a study in rhesus monkeys, The Lancet, 362 (2003), 1953-1958.
doi: 10.1016/S0140-6736(03)15012-X. |
| [11] |
Ministry of Health, Uganda, Uganda Hospital and Health Centre IV Census Survey, 2014,198. Google Scholar |
| [12] |
P. Kazanjian, Ebola in antiquity, Clinical Infectious Disease, 61 (2015), 963-968. Google Scholar |
| [13] |
Dr. A. I. Khan, Chief Physician and Head, Hospitals, icddr, b, Dhaka, Bangladesh, Personal communication, October 11, 2017. Google Scholar |
| [14] |
Medecins Sans Frontieres, International Response to West Africa Ebola Epidemic Dangerously Inadequate, August 15, 2014. https://www.msf.org/international-response-west-africa-ebola-epidemic-dangerously-inadequate, Access date: 2018-06-01. Google Scholar |
| [15] |
Sylvie Diane Djiomba Njankou and Farai Nyabadza, Modelling the potential impact of limited hospital beds on Ebola virus disease dynamics, Mathematical Methods in the Applied Sciences, (2018), 1-17. Google Scholar |
| [16] |
World Health Organization, Ebola Situation Report, June 10, 2016. http://who.int/csr/disease/ebola/en/. Google Scholar |
| [17] |
World Health Organization, Health Statistics and Information Systems, Update date: 07-01-2016, http://www.who.int/healthinfo/global_burden_disease/metrics_daly/en/, Access date: 03-03-2017. Google Scholar |
| [18] |
World Health Organization, Liberia: Ebola Treatment Centre Sets A New Pace, October 2014. http://www.who.int/features/2014/liberia-ebola-island-clinic/en/, Access date 2018-06-01. Google Scholar |
| [19] |
World Health Organization, Why the Ebola outbreak has been underestimated, August 22, 2014. http://www.who.int/mediacentre/news/ebola/22-august-2014/en/, Access date 2018-06-01. Google Scholar |
| [20] |
E. Qin, J. Bi, M. Zhao, Y. Wang, T. Guo, T. Yan, Z. Li, J. Sun, J. Zhang, S. Chen, Y. Wu, J. Li and Y. Zhong,
Clinical features of patients with Ebola virus disease in Sierra Leone, Clinical Infectious Diseases, 61 (2015), 491-495.
doi: 10.1093/cid/civ319. |
| [21] |
J. A. Salomon, J. A. Haagsma, A. Davis, C. M. de Noordhout, S. Polinder, A. H. Havelaar, A. Cassini, B. Devleesschauwer, M. Kretzschmar, N. Speybroeck and C. J. L. Murray, Disability weights for the Global Burden of Disease 2013 study, The Lancet, 3 (2015), 712-723. Google Scholar |
| [22] |
J. S. Schieffelin, J. G. Shaffer, A. Goba, M. Gbakie, S. K. Gire, A. Colubri, R. S. G. Sealfon, L. Kanneh, A. Moigboi, M. Momoh, M. Fullah, L. M. Moses, B. L. Brown, K. G. Andersen, S. Winnicki, S. F. Schaffner, D. J. Park, N. L. Yozwiak, P.-P. Jiang, D. Kargbo, S. Jalloh, M. Fonnie, V. Sinnah, I. French, A. Kovoma, F. K. Kamara, V. Tucker, E. Konuwa, J. Sellu, I. Mustapha, M. Foday, M. Yillah, F. Kanneh, S. Saffa, J. L. B. Massally, M. L. Boisen, L. M. Branco, M. A. Vandi, D. S. Grant, C. Happi, S. M. Gevao, T. E. Fletcher, R. A. Fowler, D. G. Bausch, P. C. Sabeti, S. H. Khan and R. F. Garry,
Clinical illness and outcomes in patients with Ebola in Sierra Leone, New England Journal of Medicine, 371 (2014), 2092-2100.
doi: 10.1056/NEJMoa1411680. |
| [23] |
National Center for Health Statistics, Health, United States, 2015: With Special Feature on Racial and Ethnic Health Disparities, Hyattsville, MD. 2016. Google Scholar |
Figure 2.
Decomposition of infected class to compute disease burden
Figure 3.
Ebola in Sierra Leone in 2014 for our hypothetical hospital setup
Figure 4.
A sensitivity analysis shows the percentage change in final cost given parameter changes of 1%. Parameters are ranked here by magnitude of impact
Figure 5.
Total loss comparison for two policies with varying infection rate ($\beta_c$ )
Figure 6.
Comparison of two policies as death rate ($d_c$ ) changes
Figure 7.
Policy comparison in terms of total loss with varying recovery rate
Table 1.
Estimation of the parameter $p$
Table 2.
Model parameters and their values
| Parameter | Meaning | Value |
| Infection rate in the community | 0.455/day | |
| Infection rate in the hospital | 0.004375 /person-day | |
| Recovery rate in the community | 0.04/day | |
| Recovery rate in the hospital | 0.057/day | |
| Death rate in the community | 0.172/day | |
| Death rate in the hospital | 0.102/day | |
| Patients transfer rate from community to hospital | 0.184/day | |
| Recovery rate in the hospital from primary diseases | 0.067/day | |
| Carrying capacity of the hospital | 40 beds | |
| Scaling parameter for deterio- ration of the hospital setting under overcrowded scenario | 0.48067 |
| Parameter | Meaning | Value |
| Infection rate in the community | 0.455/day | |
| Infection rate in the hospital | 0.004375 /person-day | |
| Recovery rate in the community | 0.04/day | |
| Recovery rate in the hospital | 0.057/day | |
| Death rate in the community | 0.172/day | |
| Death rate in the hospital | 0.102/day | |
| Patients transfer rate from community to hospital | 0.184/day | |
| Recovery rate in the hospital from primary diseases | 0.067/day | |
| Carrying capacity of the hospital | 40 beds | |
| Scaling parameter for deterio- ration of the hospital setting under overcrowded scenario | 0.48067 |
Table 3.
Summary of the epidemic for both policies: Continue to admit patients (policy Ⅰ) or limit admissions to the carrying capacity (policy Ⅱ)
| Policy | Infections | Deaths | Uninfected |
| Ⅰ | 98, 486 | 79, 844 | 1514 |
| Ⅱ | 98, 518 | 79, 827 | 1482 |
| Policy | Infections | Deaths | Uninfected |
| Ⅰ | 98, 486 | 79, 844 | 1514 |
| Ⅱ | 98, 518 | 79, 827 | 1482 |
| [1] |
Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete & Continuous Dynamical Systems - B, 2013, 18 (1) : 37-56. doi: 10.3934/dcdsb.2013.18.37 |
| [2] |
Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595-607. doi: 10.3934/mbe.2007.4.595 |
| [3] |
Gerardo Chowell, R. Fuentes, A. Olea, X. Aguilera, H. Nesse, J. M. Hyman. The basic reproduction number $R_0$ and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1455-1474. doi: 10.3934/mbe.2013.10.1455 |
| [4] |
Tom Burr, Gerardo Chowell. The reproduction number $R_t$ in structured and nonstructured populations. Mathematical Biosciences & Engineering, 2009, 6 (2) : 239-259. doi: 10.3934/mbe.2009.6.239 |
| [5] |
Ling Xue, Caterina Scoglio. Network-level reproduction number and extinction threshold for vector-borne diseases. Mathematical Biosciences & Engineering, 2015, 12 (3) : 565-584. doi: 10.3934/mbe.2015.12.565 |
| [6] |
Gerardo Chowell, Catherine E. Ammon, Nicolas W. Hengartner, James M. Hyman. Estimating the reproduction number from the initial phase of the Spanish flu pandemic waves in Geneva, Switzerland. Mathematical Biosciences & Engineering, 2007, 4 (3) : 457-470. doi: 10.3934/mbe.2007.4.457 |
| [7] |
Tianhui Yang, Lei Zhang. Remarks on basic reproduction ratios for periodic abstract functional differential equations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (12) : 6771-6782. doi: 10.3934/dcdsb.2019166 |
| [8] |
Svend Christensen, Preben Klarskov Hansen, Guozheng Qi, Jihuai Wang. The mathematical method of studying the reproduction structure of weeds and its application to Bromus sterilis. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 777-788. doi: 10.3934/dcdsb.2004.4.777 |
| [9] |
Mariantonia Cotronei, Tomas Sauer. Full rank filters and polynomial reproduction. Communications on Pure & Applied Analysis, 2007, 6 (3) : 667-687. doi: 10.3934/cpaa.2007.6.667 |
| [10] |
IvÁn Area, FaÏÇal NdaÏrou, Juan J. Nieto, Cristiana J. Silva, Delfim F. M. Torres. Ebola model and optimal control with vaccination constraints. Journal of Industrial & Management Optimization, 2018, 14 (2) : 427-446. doi: 10.3934/jimo.2017054 |
| [11] |
Donatella Donatelli, Bernard Ducomet, Šárka Nečasová. Low Mach number limit for a model of accretion disk. Discrete & Continuous Dynamical Systems - A, 2018, 38 (7) : 3239-3268. doi: 10.3934/dcds.2018141 |
| [12] |
Sabri Bensid, Jesús Ildefonso Díaz. On the exact number of monotone solutions of a simplified Budyko climate model and their different stability. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1033-1047. doi: 10.3934/dcdsb.2019005 |
| [13] |
Madhu Jain, Sudeep Singh Sanga. Admission control for finite capacity queueing model with general retrial times and state-dependent rates. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-25. doi: 10.3934/jimo.2019073 |
| [14] |
Timothy C. Reluga, Jan Medlock, Alison Galvani. The discounted reproductive number for epidemiology. Mathematical Biosciences & Engineering, 2009, 6 (2) : 377-393. doi: 10.3934/mbe.2009.6.377 |
| [15] |
Michel Laurent, Arnaldo Nogueira. Rotation number of contracted rotations. Journal of Modern Dynamics, 2018, 12: 175-191. doi: 10.3934/jmd.2018007 |
| [16] |
Scott W. Hansen. Controllability of a basic cochlea model. Evolution Equations & Control Theory, 2016, 5 (4) : 475-487. doi: 10.3934/eect.2016015 |
| [17] |
Aili Wang, Yanni Xiao, Huaiping Zhu. Dynamics of a Filippov epidemic model with limited hospital beds. Mathematical Biosciences & Engineering, 2018, 15 (3) : 739-764. doi: 10.3934/mbe.2018033 |
| [18] |
Jean-Paul Chehab, Alejandro A. Franco, Youcef Mammeri. Boundary control of the number of interfaces for the one-dimensional Allen-Cahn equation. Discrete & Continuous Dynamical Systems - S, 2017, 10 (1) : 87-100. doi: 10.3934/dcdss.2017005 |
| [19] |
Thomas Alazard. A minicourse on the low Mach number limit. Discrete & Continuous Dynamical Systems - S, 2008, 1 (3) : 365-404. doi: 10.3934/dcdss.2008.1.365 |
| [20] |
Wilfrid Gangbo, Andrzej Świech. Optimal transport and large number of particles. Discrete & Continuous Dynamical Systems - A, 2014, 34 (4) : 1397-1441. doi: 10.3934/dcds.2014.34.1397 |
2018 Impact Factor: 1.313
Tools
Metrics
Other articles
by authors
[Back to Top]