Mathematical models for the population dynamics of de novo resistant Mycobacterium tuberculosis within individuals are studied. The models address the use of one or two antimicrobial drugs for treating latent tuberculosis (TB). They consider the effect of varying individual immune response strength on the dynamics for the appearance of resistant bacteria. From the analysis of the models, equilibria and local stabilities are determined. For assessing temporal dynamics and global stability for sensitive and drug-resistant bacteria, numerical simulations are used. Results indicate that for a low bacteria load that is characteristic of latent TB and for small reduction in an immune response, the use of a single drug is capable of curing the infection before the appearance of drug resistance. However, for severe immune deficiency, the use of two drugs will provide a larger time period before the emergence of resistance. Therefore, in this case, two-drugs treatment will be more efficient in controlling the infection.
In the study of the black holes with Higgs field appears in a natural way the Lotka-Volterra differential systeṁ x = x(y − 1),ẏ = y(1 + y − 2x 2 − z 2),ż = zy, in R 3. Here we provide the qualitative analysis of the flow of this system describing the α-limit set and the ω-limit set of all orbits of this system in the whole Poincaré ball, i.e. we identify R 3 with the interior of the unit ball of R 3 centered at the origin and we extend analytically this flow to its boundary, i.e. to the infinity.
Applying the averaging theory of first, second and third order to one class generalized polynomial Liénard differential equations, we improve the known lower bounds for the maximum number of limit cycles that this class can exhibit.
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