Accurate forecasts of the effectiveness of interventions against Ebola may require models that account for variations in symptoms during infection

Epidemiological models are routinely used to predict the effects of interventions aimed at reducing the impacts of Ebola epidemics. Most models of interventions targeting symptomatic hosts, such as isolation or treatment, assume that all symptomatic hosts are equally likely to be detected. In other words, following an incubation period, the level of symptoms displayed by an individual host is assumed to remain constant throughout an infection. In reality, however, symptoms vary between different stages of infection. During an Ebola infection, individuals progress from initial non-specific symptoms through to more severe phases of infection. Here we compare predictions of a model in which a constant symptoms level is assumed to those generated by a more epidemiologically realistic model that accounts for varying symptoms during infection. Both models can reproduce observed epidemic data, as we show by fitting the models to data from the ongoing epidemic in the Democratic Republic of Congo and the 2014-16 epidemic in Liberia. However, for both of these epidemics, when interventions are altered identically in the models with and without levels of symptoms that depend on the time since first infection, predictions from the models differ. Our work highlights the need to consider whether or not varying symptoms should be accounted for in models used by decision makers to assess the likely efficacy of Ebola interventions.


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Intervention testing. A range of alternative control interventions are introduced into the fitted model, and 59 predicted dynamics under these new control interventions can be observed -predictions of the effects of 60 reduced surveillance (green), slightly intensified surveillance (blue) and significantly intensified surveillance ( ) = 8 9 for ≤ days, * for > days.
We then considered two alternative versions of the model. In the first (the constant 169 symptoms model -Fig 2A), we assumed that all infectious individuals are successfully 170 detected and isolated at the same average rate per day, so that δ * = δ , = δ -= δ, say. 171 This assumption is common to any epidemiological model that includes interventions 172 aimed at symptomatic hosts, unless differences in symptom expression are accounted 173 for explicitly. The constant symptoms model is therefore similar to most epidemiological 174 models that have been used to represent Ebola epidemics previously (e.g. [4,13]). 175 176 We also considered the more realistic case in which symptoms become more severe as 177 infection progresses, so that δ * < δ , < δ -. We refer to the resulting model as the 178 variable symptoms model (Fig 2B). This model reflects the fact that, in reality, 179 individuals with initial mild symptoms are less likely to be detected and isolated to 180 prevent further transmission than individuals with more developed symptoms who are in 181 the gastrointestinal or deterioration phases. 182  The default parameter values used in our analyses are given in However, as described in the Results, we also checked the robustness of our results to 200 these particular parameter values. The values of the infection rates 9 and * , as well as 201 the date on which the infection rate changes, , were obtained by fitting the outputs of 202 the models to the epidemic data. The start date of the epidemic, 9 , was also estimated 203 during the fitting procedure. Model fitting was performed using least squares estimation 204 -i.e. choosing parameter values to minimise the sum of squares distance between the 205 cumulative numbers of detected or removed hosts in the model (C + R) and the 206 cumulative numbers of cases in the data. Numerical solutions were generated starting 207 with a single host in the E compartment at the start time of the epidemic, 9 , with all 208 other individuals susceptible. 209

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The values of the parameters characterising the rate of Ebola detection and isolation, 211 i.e. δ * , δ , and δ -, depend on the level of surveillance, which includes various passive 212 and active case finding strategies. We did not model explicitly the wide range of 213 different surveillance activities that take place during an Ebola response (see In our main analyses, we considered two different surveillance regimes. When the 226 models were fitted, under weak surveillance, we assumed that the default surveillance 227 period was ∆ = 21 days. When the fitted models were then used to predict the impacts 228 of intensified surveillance, the surveillance period was changed to ∆ = 14 days. We 229 assumed that the detection probability in the constant symptoms model was * = , = 230 -= 0.6. When we accounted for the possibility that symptoms change as hosts 231 progress through infection, we instead used default values of * = 0.1, , = 0.8 and 232 -= 0.9 so that the mean value of * , , andwas equal to the value of these 233 parameters in the constant symptoms model. In other words, conditional on not being 234 detected previously, a host chosen at a random time in the infectious period was equally 235 likely to be detected in both models. 236 237 3. RESULTS 238 239 As described in the Introduction, fitted models are often used to test potential control 240 interventions (Fig 1). We therefore considered fitting models to two different datasets - of Congo (Fig 3A). We fitted the constant symptoms model and variable symptoms 246 model to these data in turn, and found that both of these models could replicate the 247 observed dynamics of the epidemic (Figs 3B). We then used these fitted models to 248 predict how the epidemic dynamics would have been altered under a different control 249 intervention. In particular, we increased the rate of detection in the fitted models, to 250 represent predictions under an intensification of surveillance and control efforts (see 251

Methods). 252 253
When surveillance was intensified, the prediction of the constant symptoms model 254 differed substantially from that of the variable symptoms model (Fig 3C). In particular, 255 for the parameter values displayed here, the constant symptoms model predicted 24% 256 fewer cases than the more epidemiologically realistic variable symptoms model (108 257 cases in the constant symptoms model as opposed to 142 cases in the variable 258 symptoms model). Consequently, even though the observed dynamics of the models appear identical when fitted to data, they produce different predictions when control 260 interventions are changed. 261 We then repeated our analysis, instead using data from the 2014-16 Ebola epidemic in 263 west Africa (Figs 3D-F). In this case, the constant symptoms model predicted 35% 264 fewer cases than the variable symptoms model (Fig 3F). Since the total number of 265 cases in this epidemic was so large, this corresponded to 641 cases difference between 266 the forecasts of the two models.   We parameterised our models using the simplest possible approach -namely fitting the 421 numbers of detected or removed individuals in the relevant classes of the models to 422 data on the cumulative numbers of symptomatic cases using least squares estimation. 423 We did not quantify the uncertainty in estimates of the values of model parameters, 424 since the precise method of parameter inference was not central to our message. 425 Instead, we sought to use the simplest possible fitting method. While this approach is 426 used frequently during epidemics due to its ability to produce quick forecasts [5,36,37], to properly quantify the uncertainty in forward projections it would be necessary to use 428 non-cumulative incidence data and fit stochastic transmission models [38]. 429

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One advantage of the models that we used is that the surveillance level is assumed to 431 impact on the epidemiological dynamics themselves, rather than simply the observed 432 dynamics. This is not always the case in epidemiological models: a common method for 433 accounting for under-reporting is simply to scale the incidence data up