Abstract
The deadly infectious Ebola incidences scare not only to the residents of western Africa but also to the travelers and medical professionals who treat the patients, as they became victims. Since 27 July until 13 August 2014 alone, about 2,127 Ebola cases occurred in just four Western African countries: Guinea, Liberia, Nigeria and Sierra Leone and more than 50% of them died. The mortality is extremely higher. No known medication exists. Though the virus is not airborne spreading, a contact with the patient’s fluids, tissues, or bodies is known to transmit Ebola virus. There had been three categories: Suspected, probable, or confirmed in the collection of Ebola incidences and deaths. Their data are quite informative if they are properly processed and it is exactly the aim of this article. For this purpose, the stochastic nature of the data is probed rationally. The Ebola incidences and deaths in each category exhibit a separate Poisson chance environment and yet, they are connected. Therefore, suitable Poisson models are developed for each category and are then woven together to analyse the entire pertinent data on Ebola incidences and deaths in those four countries. Pictures are worth the thousand words to comprehend non-trivial findings. Hence, innovatively the data analytic concepts for three-dimensional sphere for each country is developed and applied. By superimposing the four spheres (one for each country), this article points out the relative performance of the four countries with respect to the Ebola incidences and deaths together in each category. One country does better than others in one category but poorly in other two categories. A better performance by a country is a reflection of effective prevention and successful medical treatment of Ebola cases.
Highlights
We need to first identify an underlying probability pattern of the number of Ebola cases based on the number of Ebola deaths
The result (12) implies that the conditional projection of the number of Ebola incidences based on the number of Ebola deaths starts at z with an increment (1-φ), which is the survival chance from
The conditional projection of the number of Ebola cases based on knowing the number of Ebola deaths or vice versa has an efficiency level (1-φ), which happens to be the survival chance from Ebola epidemic
Summary
Ebola is a deadly infectious disease and it is a nightmare even to the medical professionals, as some of them treating the patients became its victims. From the joint probability distribution (3), the marginal probability distribution of the number of Ebola deaths in a region during a period is obtained and it is parameters compounded Poisson distribution:. The MLE of the Ebola mortality rate in the suspected, probable and confirmed category are z z z respectively φs = s , φp = p and φc = c , where zs zs ys yp yc and zs are respective average number of Ebola deaths in the suspected, probable and confirmed category. Zs = 0,1, 2,..., ∞;θ > 0;0 < π s < 1;0 < φs < 1 and Yc be respectively the number of Ebola suspect, probable and confirmed cases. In. A resident in the region with Ebola epidemic incidence rate θ might encounter the virus and becomes one of three orderly possibilities: Suspect, probable, or confirmed. When the person shows symptoms as described in the motivation section, s/he becomes an
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