Abstract

A BRANCHING PROCESS MODEL TO SIMULATE EBOLA EPIDEMICS

1O. Abu and 2P.N. Okolo

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Abstract Ebola virus disease is dreadful and, therefore, the study of its transmission process is worthwhile. In this paper, a discrete Galton-Watson branching process model is applied to simulate Ebola epidemics in a population. The data on secondary transmissions in countries where new cases were reported were classified according to the control response: delayed or immediate. The basic reproduction numbers R_0 s were estimated for three classes: one for delayed control with R_0=2.857 and two for immediate control with R_0 s of 0.1724 and 0.05. Simulations for these scenarios were carried out to determine the spread on generation basis up to the 10th generation. The results showed that delayed control of an index case can cause a major outbreak with probability 1. On the other hand, immediate control can stop an outbreak with probability 1. The results further showed that the probability of extinction for an index case that experiences delay in control is zero by 10th generation. However, the probability of extinction for an index case with? R?_0=0.1724 is 1 by the 3rd generation; and the probability of extinction for an index case withR_0=0.05 is 1 by 3rd generation. The findings of this study suggest that immediate control is crucial to stopping Ebola outbreak. Key words: Branching process, ebola virus, index case, Galton-Watson process, probability generating function

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