Seven years after the declaration of the first epidemic of Ebola virus disease in Guinea, the country faced a new outbreak-between 14 February and 19 June 2021-near the epicentre of the previous epidemic 1,2 . Here we use next-generation sequencing to generate complete or near-complete genomes of Zaire ebolavirus from samples obtained from 12 different patients. These genomes form a well-supported phylogenetic cluster with genomes from the previous outbreak, which indicates that the new outbreak was not the result of a new spillover event from an animal reservoir. The 2021 lineage shows considerably lower divergence than would be expected during sustained human-to-human transmission, which suggests a persistent infection with reduced replication or a period of latency. The resurgence of Zaire ebolavirus from humans five years after the end of the previous outbreak of Ebola virus disease reinforces the need for long-term medical and social care for patients who survive the disease, to reduce the risk of re-emergence and to prevent further stigmatization.At least 30 outbreaks of Ebola virus disease (EVD) have been identified since the late 1970s, the most severe of which affected Guinea, Sierra Leone and Liberia from December 2013 to June 2016 1,2 . Guinea experienced a new outbreak of EVD in 2021, which started in Gouéké-a town about 200 km away from the epicentre of the 2013-2016 outbreak. The probable index case was a 51-year-old nurse, an assistant of the hospital midwife in Gouéké. On 21 January 2021, she was admitted to hospital in Gouéké suffering from headache, asthenia, nausea, anorexia, vertigo and abdominal pain. She was diagnosed with malaria and salmonellosis and was released two days later. Feeling ill again once at home, she attended a private clinic in Nzérékoré (40 km away) and visited a traditional healer, but died three days later. In the week after her death, her husband-as well as other family members who attended her funeral-fell ill, and four of them died. They were reported as the first suspect cases by the national epidemic alert system on 11 February. On 12 February, blood was taken from two suspect cases admitted to
This paper is concerned with the stability problem for the planar linear switched systemẋ(t) = u(t)A1x(t)+(1−u(t))A2x(t), where the real matrices A1, A2 ∈ R 2×2 are Hurwitz and u(·) : [0, ∞[→ {0, 1} is a measurable function. We give coordinate-invariant necessary and sufficient conditions on A1 and A2 under which the system is asymptotically stable for arbitrary switching functions u(·). The new conditions unify those given in previous papers and are simpler to be verified since we are reduced to study 4 cases instead of 20. Most of the cases are analyzed in terms of the function Γ(A1, A2) = 1 2 (tr(A1)tr(A2) − tr(A1A2)).
The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a large class of switched systems are asymptotically stable. For this purpose we define what we call non chaotic inputs, which generalize the different notions of inputs with dwell time.Next we turn our attention to the behaviour for possibly chaotic inputs. To finish we give a sufficient condition for a system composed of a pair of Hurwitz matrices to be asymptotically stable for all inputs.
Consider the planar linear switched systemẋ(t) = u(t)Ax(t) + (1 − u(t))Bx(t), where A and B are two 2×2 real matrices, x ∈ R 2 , and u(.) : [0, ∞[→ {0, 1} is a measurable function. In this paper we consider the problem of finding a (coordinate-invariant) necessary and sufficient condition on A and B under which the system is asymptotically stable for arbitrary switching functions u(.).This problem was solved in previous works under the assumption that both A and B are diagonalizable. In this paper we conclude this study, by providing a necessary and sufficient condition for asymptotic stability in the case in which A and/or B are not diagonalizable.To this purpose we build suitable normal forms for A and B containing coordinate invariant parameters. A necessary and sufficient condition is then found without looking for a common Lyapunov function but using "worst-trajectory" type arguments.
We present a mathematical model of a fishery on several sites with a variable price. The model takes into account the evolution during the time of the resource, fish and boat movement between the different sites, fishing effort and price that varies with respect to supply and demand. We suppose that the movements of the boats and resource as well as the variation of the price go on at a fast time scale. We use methods of aggregation of variables in order to reduce the number of variables and we derive a reduced model governing two global variables, respectively the biomass of the resource and the fishing effort of the whole fishery. We look for the existence of equilibria of the aggregated model and perform local stability analysis. Two main cases can occur. The first one corresponds to over-exploitation leading to fish extinction. At extinction, the fishing effort tends to a positive value. The second case corresponds to a durable fishery equilibrium which is globally asymptotically stable. In the later case, we show that there exists a number of fishing sites that optimizes the total catch of the fishery.
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