Abstract: We present a deterministic model which describes
the dynamics of tuberculosis in Algerian population where the
vaccination program with BCG is in place since 1969 and where
the WHO recommendations regarding the DOTS (directly-observed
treatment, short course) strategy are in application. The impact
of an intervention program, targeting recently infected people
among all close contacts of active cases and their treatment to
prevent endogenous reactivation, on the incidence of tuberculosis,
is investigated. We showed that a widespread treatment of latently
infected individuals for some years is recommended to shift from
higher to lower equilibrium state and thereafter relaxation is
recommended.
Abstract: According to Hermite there exists only a finite
number of number fields having a given degree, and a given value of
the discriminant, nevertheless this number is not known generally.
The determination of a maximum number of number fields of degree
10 having a given discriminant that contain a subfield of degree 5
having a fixed class number, narrow class number and Galois group
is the purpose of this work. The constructed lists of the first
coincidences of 52 (resp. 50, 40, 48, 22, 6) nonisomorphic number
fields with same discriminant of degree 10 of signature (6,2) (resp.
(4,3), (8,1), (2,4), (0,5), (10,0)) containing a quintic field. For each
field in the lists, we indicate its discriminant, the discriminant of its
subfield, a relative polynomial generating the field over its quintic
field and its relative discriminant, the corresponding polynomial over
Q and its Galois closure are presented with concluding remarks.