利用SIR模型预测埃博拉疫情——美国疾病控制中心报告

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"SIR模型是疾病控制中心(CDC)用于模拟和预测疾病传播的重要工具，如在2014-2015年期间对利比里亚和塞拉利昂埃博拉疫情的估计。该模型由CDC利用Microsoft Excel 2010构建，并在公开的电子表格中提供。通过这个模型，CDC能够估算出未来病例的数量，以支持公共卫生决策和应对措施。" "SIR模型"是一种流行病学模型，用于研究传染病在人群中的传播动态。SIR代表三个关键的群体状态：易感者(Susceptible)、感染者(Infectious)和康复者(Recovered)。在这个模型中，易感者可以被感染，感染者会传播疾病，而康复者则获得免疫力，不再参与疾病传播。 - 易感者(S)：这是没有接触过病原体，对疾病无免疫力的人群。他们可以通过与感染者的接触而成为新的感染者。 - 感染者(I)：已经接触到病原体并正在传播疾病的人。他们在模型中是疾病的主要载体。 - 康复者(R)：包括治愈的患者和因疾病死亡的人。这些人不再具有传染性，可能对特定疾病有免疫力。 SIR模型的核心在于理解和计算这三个群体之间的转换速率。这些速率通常表示为β（易感者转化为感染者的速率）、γ（感染者康复或死亡的速率）。模型通过微分方程来描述这些群体随时间的变化，帮助预测疾病的传播趋势和可能的感染峰值。在应对埃博拉疫情时，CDC利用SIR模型估计了病例增长，这涉及到对传播率、康复率、人口结构、隔离措施效果等多因素的综合考虑。这种预测有助于规划资源分配、医疗设施的建设和疫苗接种策略。同时，模型结果也可为政策制定者提供科学依据，以便采取适当的干预措施，控制疾病扩散。 "MMWR"（Morbidity and Mortality Weekly Report）是美国疾病控制与预防中心出版的一份报告，它发布关于公共卫生事件和疾病监测的数据和分析。报告中提到的"Estimating the Future Number of Cases in the Ebola Epidemic—Liberia and Sierra Leone, 2014–2015"是专门针对埃博拉疫情的研究，提供了早期发布的数据和分析结果，以指导当时的公共卫生响应。 SIR模型是疾病控制中心在应对传染病时的重要工具，通过它能进行疫情预测，为决策者提供关键信息，以制定有效的防控策略。在这个案例中，CDC利用Excel构建的SIR模型成功预测了埃博拉疫情的发展，为全球公共卫生事业提供了有力的支持。

2 MMWR / September 26, 2014 / Vol. 63 / No. 3

Supplement

persons were assumed to eventually become symptomatic.

Data from reports of previous Ebola outbreaks were used to

model the daily change of patients’ status between the disease

states. For example, a probability distribution to characterize

the likelihood of incubating a given number of days was built

using previously published data (4). The resulting distribution

has a mean incubation period of approximately 6 days and a

99th percentile of 21 days (Appendix [Figure 4]). Based on

previous studies, patients were assumed to be infectious for a

period of 6 days (3,5).

Patients were categorized into three levels: 1) hospitalized

in an Ebola treatment unit (ETU) or medical care facility,

2) home or in a community setting such that there is a reduced

risk for disease transmission (including safe burial when

needed), and 3) home with no effective isolation (Appendix

[Figure 5]). Hospitalized refers to facilities such as ETUs where

medical care is provided. Ideally, such facilities have infection-

control protocols that prevent additional disease transmission.

However, this is not always the case. Therefore, the average

daily risk for transmission is greater than zero in these facilities

(i.e., transmission does occur), but the risk is fewer than one

person infected per infectious patient (Appendix [Table 1]).

The risk for onward disease transmission by patient category

was calculated (Appendix [Table 1]). The ability to add

imported cases (whole numbers) every 10 days (approximately

the sum of the average incubation and infectiousness periods)

was built into the EbolaResponse modeling tool (Appendix

[Table 2]). Imported cases represent either cases in persons who

travel into the community undetected from other outbreak-

affected areas or persons who might represent previously

undetected chains of transmission. To estimate the daily

number of beds in use (i.e., beds in medical care facilities, such

as ETUs), previously published data were adapted to provide

both the likelihood of a patient going to an ETU and the

number of days that a patient in each patient category would

spend in the hospital (6) (Appendix [Table 3]).

Substantial underreporting of cases might be occurring both

in Liberia and Sierra Leone (7). To correct for underreporting,

EbolaResponse was used to predict the number of beds in use

on August 28, 2014. This number was then compared with the

actual number of beds in use (from expert opinion estimates).

The difference between the two estimates is the potential

underreporting correction factor of 2.5 (Appendix [Table 4]).

Accuracy of the estimates produced by EbolaResponse was

assessed by comparing the model-predicted number of cases

to the reported cases (Appendix [Figure 6, Table 5]). The

difference in estimates calculated using the uncorrected data

and the estimates using the data corrected for underreporting

reflects the potential range of uncertainty regarding the actual

number of cases that might occur.

Accuracy of the model forecasts was tested by comparing the

latest available reported cases at time of writing to estimated

cases (estimated using uncorrected data). The last date of

reported data used to fit the model was August 28, 2014, for

Sierra Leone and August 29, 2014, for Liberia. Reported cases

were compared with estimated cases as of September 9, 2014,

for Liberia and September 13, 2014, for Sierra Leone.

In the absence of a universal preventive intervention (e.g.,

vaccine), control of the epidemic consists of having as many

patients as possible receiving care in hospitals or, when ETUs

are at capacity, at home or in a community setting such that

there is a reduced risk for disease transmission (including safe

burial when needed). Suitable methods to enhance protection

and minimize disease transmission are under development. To

illustrate how increasing the percentage of patients in these

two categories can control and eventually end the epidemic in

Liberia, the first scenario was created. Starting on August 24,

2014, and for the following 30 days, the percentage of patients

in ETUs was increased from 10% of all patients to 17%. In

the subsequent 30 days (starting September 23, 2014), that

percentage was increased to 25% and left at that level for the

remainder of the period covered by the model (Appendix

[Figure 7, Figure 8]). Starting on August 24, 2014, and for the

following 30 days, the percentage of patients at home or in a

community setting such that there is a reduced risk for disease

transmission was increased from 8% of all patients to 20%.

Additional increases were included so that by December 22,

2014, a total of 70% of patients were in either one of the

two patient settings (25% in ETUs and 45% at home or in a

community setting such that there is a reduced risk for disease

transmission) (Appendix [Figure 8]).

To illustrate the cost of delay, in terms of additional cases and

the resulting need for additional resources to end the epidemic, in

starting to increase interventions that can control and eventually

stop the epidemic, a second separate control-and-stop scenario

was first constructed as follows. Starting on September 23, 2014,

and for the next 30 days, the percentage of all patients in ETUs

was increased from 10% to 13%. This percentage was again

increased on October 23, 2014, to 25%, on November 22, 2014,

to 40%, and finally on December 22, 2014, to 70% (Appendix

[Figure 9]) (i.e., it takes 90 days for the percentage of patients in

ETUs to reach 70% of all patients). The percentage of patients

at home or in a community setting such that there is a reduced

risk for disease transmission was kept at 8% from September 23,

2014, through the remainder of the period covered by the model.

The impact of delay of starting the increase in interventions was

then estimated by twice repeating the above scenario but setting

the start day on either October 23, 2014, or November 22, 2014.

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