BackgroundEbola virus disease has reemerged as a major public health crisis in Africa, with isolated cases also observed globally, during the current outbreak.MethodsTo estimate the basic reproductive ratio R0, which is a measure of the severity of the outbreak, we developed a SEIR (susceptible-exposed-infected-recovered) type deterministic model, and used data from the Centers for Disease Control and Prevention (CDC), for the Ebola outbreak in Liberia and Sierra Leone. Two different data sets are available: one with raw reported data and one with corrected data (as the CDC suspects under-reporting).ResultsUsing a deterministic ordinary differential equation transmission model for Ebola epidemic, the basic reproductive ratio R0 for Liberia resulted to be 1.757 and 1.9 for corrected and uncorrected case data, respectively. For Sierra Leone, R0 resulted to be 1.492 and 1.362 for corrected and uncorrected case data, respectively. In each of the two cases we considered, the estimate for the basic reproductive ratio was initially greater than unity leading to an epidemic outbreak.ConclusionWe obtained robust estimates for the value of R0 associated with the 2014 Ebola outbreak, and showed that there is close agreement between our estimates of R0. Analysis of our model also showed that effective isolation is required, with the contact rate in isolation less than one quarter of that for the infected non-isolated population, and that the fraction of high-risk individuals must be brought to less than 10% of the overall susceptible population, in order to bring the value of R0 to less than 1, and hence control the outbreak.Electronic supplementary materialThe online version of this article (doi:10.1186/s40249-015-0043-3) contains supplementary material, which is available to authorized users.
We formulate a deterministic epidemic model for the spread of Corona Virus Disease . We have included asymptomatic, quarantine and isolation compartments in the model, as studies have stressed upon the importance of these population groups on the transmission of the disease. We calculate the basic reproduction number R 0 and show that for R 0 < 1 the disease dies out and for R 0 > 1 the disease is endemic. Using sensitivity analysis we establish that R 0 is most sensitive to the rate of quarantine and isolation and that a high level of quarantine needs to be maintained as well as isolation to control the disease. Based on this we devise optimal quarantine and isolation strategies, noting that high levels need to be maintained during the early stages of the outbreak. Using data from the Wuhan outbreak, which has nearly run its course we estimate that R 0 = 1.87 which while in agreement with other estimates in the literature is on the lower side.
This paper was accepted to the AER under the guidance of Stefano DellaVigna, Coeditor. This project is the result of collaboration among many people. We thank Robert Gibbons, Parag Pathak, and numerous seminar participants for helpful comments. We thank
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