Predicting and Evaluating the Epidemic Trend of Ebola Virus Disease in the 2014-2015 Outbreak and the Effects of Intervention Measures

<div><p>We constructed dynamic Ebola virus disease (EVD) transmission models to predict epidemic trends and evaluate intervention measure efficacy following the 2014 EVD epidemic in West Africa. We estimated the effective vaccination rate for the population, with basic reproduction number (<i>R</i>₀) as the intermediate variable. Periodic EVD fluctuation was analyzed by solving a Jacobian matrix of differential equations based on a SIR (susceptible, infective, and removed) model. A comprehensive compartment model was constructed to fit and predict EVD transmission patterns, and to evaluate the effects of control and prevention measures. Effective EVD vaccination rates were estimated to be 42% (31–50%), 45% (42–48%), and 51% (44–56%) among susceptible individuals in Guinea, Liberia and Sierra Leone, respectively. In the absence of control measures, there would be rapid mortality in these three countries, and an EVD epidemic would be likely recur in 2035, and then again 8~9 years later. Oscillation intervals would shorten and outbreak severity would decrease until the periodicity reached ~5.3 years. Measures that reduced the spread of EVD included: early diagnosis, treatment in isolation, isolating/monitoring close contacts, timely corpse removal, post-recovery condom use, and preventing or quarantining imported cases. EVD may re-emerge within two decades without control and prevention measures. Mass vaccination campaigns and control and prevention measures should be instituted to prevent future EVD epidemics.</p></div

Compartment transfer block diagram of the transmission dynamic model.

<p>(A) Compartment transfer block diagram of the SIR model. Blocks <i>S</i>, <i>I</i>, and <i>R</i> represent susceptible individuals, symptomatic patients, and people with immunity owing to recovery, respectively. <i>β</i> is the standard contact rate, indicating the number of people infected by the same patient per unit time in a population of entirely susceptible persons. <i>α</i> and <i>γ</i> denote the probability of one patient dying or recovering per unit time, respectively. <i>b</i> and <i>d</i> are the population’s birth and mortality rates per unit time, respectively. (B) Comprehensive compartment transfer block diagram of EVD epidemiology. Blocks <i>S</i>, <i>E</i>, <i>I</i>, and <i>D</i> represent susceptible persons in a free environment, infected individuals in the incubation period, patients in a free environment, and not-yet-decontaminated corpses of EVD patients, respectively. Blocks <i>U</i>, <i>P</i>, and <i>Q</i> denote suspected cases in isolation, confirmed cases in isolation, and close contacts in isolation, respectively. Blocks <i>H</i>, <i>R</i>, <i>K</i>, and <i>A</i> indicate the medical staff in charge of <i>U</i> and <i>P</i>, recovered patients that are still infectious, recovered individuals that are not infectious and with immunity, and imported cases per day, respectively.</p

Comparison of the numbers of EVD cases and deaths predicted by the model to those published by the WHO.

<p>The cumulative number of EVD cases and deaths are plotted as a function of time <i>t</i> in months. The cumulative number of cases predicted curve (blue) includes confirmed and suspected cases. Each red point indicates the number of cumulative cases (blue curve) or deaths due to EVD (green curve) published by the WHO.</p

Periodical low dampened oscillation of <i>s</i> and <i>i</i> around the dynamic equilibrium point.

<p>The proportions of EVD cases (left y-axis) and susceptible people (right y-axis), compared to the total population, are shown as functions of time in years. In the absence of control and prevention measures, the <i>s</i> and <i>i</i> values would oscillate periodically around their dynamic equilibrium points. Meanwhile, periods between oscillations would shorten, and amplitudes would decrease gradually.</p

Effects of control and prevention measures on EVD epidemic trends.

<p>(A) Summary of the effect of isolating EVD patients’ close contacts on the cumulative number of EVD cases. Note the markedly lower curve with close contact quarantine (red) relative to that without close contact quarantine (blue). (B) Predicted numbers of cumulative EVD cases when corpses of dead EVD patients were allowed to stay in the surrounding environment for 3 (blue), 2 (green), 1 (red), or 0.5 days (yellow). (C) Predicted new EVD cases when the average symptom onset-to-isolation and treatment is 5 days (blue), 4 days (green), and 3 days (red). (D) Predicted reduction in the number of new EVD cases from August 1^st, 2014 to May 31^st, 2015 when recovered patients have condom-protected (red) versus unprotected (green) sex. (E) Summary of the effect of cases being imported from other countries on the epidemic trend of EVD. Note that introduction of a new case every other day (0.5 cases/day, green) has a strong effect on amplitude relative to zero case importation (red). In all panels, the number of predicted EVD cases is plotted as a function of time.</p

Effects of EVD on total population and EVD case number in the absence of control and prevention measures.

<p>Changes in the total number of individuals in the population and in the number of EVD cases in Guinea (A, B), Liberia (C, D), and Sierra Leone (E, F) are shown. The x-axes indicate time in months, and the y-axes indicate population number or the number of EVD cases. The shaded area indicates the 95% confidence interval.</p

Values, ranges and data sources of all parameters in models in Fig 6A and 6B.

<p>Values, ranges and data sources of all parameters in models in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0152438#pone.0152438.g006" target="_blank">Fig 6A and 6B</a>.</p