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Ebola is a world health problem and with a recent outbreak. There exist different models in the literature to predict its behavior, most of them based on data coming from previous outbreaks or using restricted number of persons in the population variable. This paper deals both with classical and fractional order SEIR (susceptible, exposed, infections, removed) Ebola epidemic model and its comparison with real data extracted from the reports periodically published by the World Health Organization (WHO), starting from March 27th, 2014. As it has been shown in the literature, one physical meaning of the fractional order in fractional derivatives is that of index of memory; and therefore, it seems to be useful for epidemic models, as in this paper. The number of confirmed cases by the WHO in its reports is used for our analysis and estimation of the parameters in our classical and fractional SEIR models. Our approach gives a good approximation to real data. Following our results, the current outbreak will continue for approximately two years, assuming that no new outbreak appears at a different community or country. Our estimates give a number of the order nine million confirmed cases. MSC: Primary 26A33; secondary 34A08

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International audienc

The purpose of this paper is to present a general view of the current applications of fuzzy logic in medicine and bioinformatics. We particularly review the medical literature using fuzzy logic. We then recall the geometrical interpretation of fuzzy sets as points in a fuzzy hypercube and present two concrete illustrations in medicine (drug addictions) and in bioinformatics (comparison of genomes).

Pulse vaccination, the repeated application of vaccine over a defined age range, is gaining prominence as an effective strategy for the elimination of infectious diseases. An SIR epidemic model with pulse vaccination and distributed time delay is proposed in this paper. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the impulsive epidemic system and prove that the infection-free periodic solution is globally attractive if the vaccination rate is larger enough. Moreover, we show that the disease is uniformly persistent if the vaccination rate is less than some critical value. The permanence of the model is investigated analytically. Our results indicate that a large pulse vaccination rate is sufficient for the eradication of the disease.

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