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# Ebola: Impact of hospital's admission policy in an overwhelmed scenario

• 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.

Mathematics Subject Classification: 92D30.

 Citation:

• Figure 1.  Flow diagram showing infection within, and transfer between, hospital and community compartments. Rates are per capita

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 $p$

 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]

Table 2.  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

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
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