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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

* Corresponding author: mdmondal.zahid@mavs.uta.edu

Received  November 09, 2017 Revised  July 19, 2018 Published  September 2018

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.

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. [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. [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. [12] P. Kazanjian, Ebola in antiquity, Clinical Infectious Disease, 61 (2015), 963-968. [13] Dr. A. I. Khan, Chief Physician and Head, Hospitals, icddr, b, Dhaka, Bangladesh, Personal communication, October 11, 2017. [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. [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. [16] World Health Organization, Ebola Situation Report, June 10, 2016. http://who.int/csr/disease/ebola/en/. [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. [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. [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. [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. [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.

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. [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. [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. [12] P. Kazanjian, Ebola in antiquity, Clinical Infectious Disease, 61 (2015), 963-968. [13] Dr. A. I. Khan, Chief Physician and Head, Hospitals, icddr, b, Dhaka, Bangladesh, Personal communication, October 11, 2017. [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. [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. [16] World Health Organization, Ebola Situation Report, June 10, 2016. http://who.int/csr/disease/ebola/en/. [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. [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. [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. [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. [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.
Flow diagram showing infection within, and transfer between, hospital and community compartments. Rates are per capita
Decomposition of infected class to compute disease burden
Ebola in Sierra Leone in 2014 for our hypothetical hospital setup
A sensitivity analysis shows the percentage change in final cost given parameter changes of 1%. Parameters are ranked here by magnitude of impact
Total loss comparison for two policies with varying infection rate ($\beta_c$)
Comparison of two policies as death rate ($d_c$) changes
Policy comparison in terms of total loss with varying recovery rate
Estimation of the parameter $p$
 Para-meter Cases Value Country Year of Epidemic Weighted Mean $p$ 61 0.20/day $(\frac{1}{5~day})$[20] Sierra Leone 2014 0.184/day 106 0.175/day $(\frac{1}{5.7~day})$[22]
 Para-meter Cases Value Country Year of Epidemic Weighted Mean $p$ 61 0.20/day $(\frac{1}{5~day})$[20] Sierra Leone 2014 0.184/day 106 0.175/day $(\frac{1}{5.7~day})$[22]
Model parameters and their values
 Parameter Meaning Value $\beta_c$ Infection rate in the community 0.455/day $\beta_H$ Infection rate in the hospital 0.004375 /person-day $\gamma_c$ Recovery rate in the community 0.04/day $\gamma_H$ Recovery rate in the hospital 0.057/day $d_c$ Death rate in the community 0.172/day $d_H$ Death rate in the hospital 0.102/day $p$ Patients transfer rate from community to hospital 0.184/day $q$ Recovery rate in the hospital from primary diseases 0.067/day $K$ Carrying capacity of the hospital 40 beds $\epsilon$ Scaling parameter for deterio- ration of the hospital setting under overcrowded scenario 0.48067
 Parameter Meaning Value $\beta_c$ Infection rate in the community 0.455/day $\beta_H$ Infection rate in the hospital 0.004375 /person-day $\gamma_c$ Recovery rate in the community 0.04/day $\gamma_H$ Recovery rate in the hospital 0.057/day $d_c$ Death rate in the community 0.172/day $d_H$ Death rate in the hospital 0.102/day $p$ Patients transfer rate from community to hospital 0.184/day $q$ Recovery rate in the hospital from primary diseases 0.067/day $K$ Carrying capacity of the hospital 40 beds $\epsilon$ Scaling parameter for deterio- ration of the hospital setting under overcrowded scenario 0.48067
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
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