AUTHOR
Maria A. Kiskowski
ABSTRACT
Background: In mid-October 2014, the number of cases of the West Africa Ebola virus epidemic in Guinea, Sierra Leone and Liberia exceeded 9,000 cases. The early growth dynamics of the epidemic has been qualitatively different for each of the three countries. However, it is important to understand these disparate dynamics as trends of a single epidemic spread over regions with similar geographic and cultural aspects, with likely common parameters for transmission rates and reproduction number R0.
Methods: We combine a discrete, stochastic SEIR model with a three-scale community network model to demonstrate that the different regional trends may be explained by different community mixing rates. Heuristically, the effect of different community mixing rates may be understood as the observation that two individuals infected by the same chain of transmission are more likely to share the same contacts in a less-mixed community. Local saturation effects occur as the contacts of an infected individual are more likely to already be exposed by the same chain of transmission.
Results: The effects of community mixing, together with stochastic effects, can explain the qualitative difference in the growth of Ebola virus cases in each country, and why the probability of large outbreaks may have recently increased. An increase in the rate of Ebola cases in Guinea in late August, and a local fitting of the transient dynamics of the Ebola cases in Liberia, suggests that the epidemic in Liberia has been more severe, and the epidemic in Guinea is worsening, due to discrete seeding events as the epidemic spreads into new communities.
Conclusions: A relatively simple network model provides insight on the role of local effects such as saturation that would be difficult to otherwise quantify. Our results predict that exponential growth of an epidemic is driven by the exposure of new communities, underscoring the importance of limiting this spread.
FUNDING STATEMENT
No external funding was received for the research. The author has declared that no competing interests exist.
INTRODUCTION
As of mid-October 2014, the number of reported suspected cases of the Ebola epidemic in West Africa had exceeded 9,000 cases, which is likely a significant underestimate 1,2,3 . Markedly different dynamical behaviors can be observed for the growth curves of the epidemic in the countries of Guinea, Sierra Leone and Liberia (Fig. 1). Most immediately, the epidemic in Liberia has been growing at a much faster rate in Liberia than in Guinea. Although the epidemic likely began much earlier in Guinea 4, Liberia had approximately the same number of cases in early August, twice as many cases by the end of August and nearly three times as many cases by mid-September. Even more striking, the number of cases in Guinea appears to have been growing sub-exponentially until late-August (approximately linearly with a slope of about 3 cases per day) while the number of cases in Liberia has been growing exponentially (approximately 10 cases per day averaged for July, 40 cases per day averaged for August and 70 cases per day in September). The growth dynamics of the epidemic in Sierra Leone appears to be intermediate between these two. It would be helpful to understand these different growth patterns within the context of a single epidemic, since a better understanding of the source of these different patterns may yield productive ideas for curbing the exponential growth of the epidemic in Liberia.
We describe a stochastic network model with three levels of community structure (households and communities of households within a country population) on which we model SEIR transmission dynamics for the spread of Ebola infection. We are able to fit the WHO Ebola case data of each country by varying only the community mixing parameter (connectivity) for each country (see Fig. 3). Observing that the long term dynamics of epidemic spread within communities are linear due to local saturation effects, we are able to demonstrate that linear growth phases followed by exponential growth phases are consistent with seeding of the epidemic to new communities.
A variety of computational and statistical models have been used help to characterize and resolve the mechanisms underlying trends in the growth of this epidemic. The models of 5 and 6 include a parameter to estimate and predict the effect of control measures on the epidemic. SEIR models such as that of 5 and 7 are four-compartment models that resolve infectious dynamics between populations based on their susceptibility and infectiousness and account for the time scales of viral incubation and infectiousness. SEIR models with seven compartments 8,9,2 further resolve the effects of varying degrees of transmission among, for example, community, hospital, and funeral populations.
These computational models focus on different aspects of the epidemic to explain or observe the marked differences of the growth curves for the epidemic in each country. The models 5 and 6, accounting for the effect of control measures, find that their models find that their models identify slowing of the growth of the epidemic only for Guinea and Sierra Leone. The model of 8 accounting for different community, hospital and funereal transmission rates, predicts that a higher number of transmissions from funerals in Liberia could account for the faster rate of growth of the epidemic in Liberia compared to Sierra Leone. Likewise, the model of 2 predicted a higher fraction of patients with no effective measures to limit transmission, including burial transmission, in Liberia. Especially interesting differences among the three countries were described by 7 in their methodology to observe changes in the effective reproductive number over time. In particular they found that the effective reproductive number rose for Liberia and Guinea. The authors observe that this increase occurred somewhat early on during the Liberia outbreak in mid-July, when the outbreak spread to densely populated regions in Monrovia, and during the Guinean outbreak in mid-August, around the time the outbreak spread to densely populated regions in Conakry.
We would like to provide a proof of principle explanation for the differences in the dynamics of the 2014 Ebola epidemic based on differences in the community network properties of the affected regions, even as the number of daily interactions, transmission rates and in particular the average number of people infected by each person R0 within a naïve population is the same for all three countries. A prediction of our model is that the effective reproductive number Re of the epidemic decreases quickly to values close to 1, indicating significant saturation effects for all three countries. Although we use a very simple homogeneous network model and our four model parameters are under-constrained, a particular choice of reasonable model parameters captures relevant average behaviors of the epidemic (for example, by fitting the growth curves of the epidemic) and we use these to interpret trends in the epidemic growth over time and between countries. A description of the roles of model parameters can be used to make predictions about the future growth of the epidemic in the context of potential epidemic controls that modify these parameters.