This paper presents a mathematical model for dynamics of HIV transmission by considering a saturated incidence type interaction for the human to human sexual transmission. The equilibria of the model are discovered, and the basic reproduction number is calculated. The analysis shows that if the basic reproduction number is less than unity, the disease-free equilibrium is locally and globally asymptotically stable. It is proved using differential equation theory and a comparison theorem. The Lyapunov function and the LaSalle invariance principle show that the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than unity. According to the sensitivity analysis, the effective contact rate was more sensitive to the basic reproduction rate than the treatment rate. The numerical simulations show that as the saturation incidence rate increases, the force of infection decreases. The prevalence of HIV/AIDS decreases as the saturation rate increases.
We study varieties of complexes of projective modules with fixed ranks, and relate these varieties to the varieties of their homologies. We show that for an algebra of global dimension at most two, these two varieties are related by a pair of morphisms which are smooth with irreducible fibres.Keywords and phrases: complexes projective varieties, algebra of global dimension at most two, homologies of complexes, smooth morphisms.
Let Λ be a finite-dimensional algebra over an algebraically closed field k. We study variety W Λ d (k) parameterizing Λ-polydules. This variety carries an action of an algebraic group such that orbits correspond to quasi-isomorphism classes of complexes in the derived category. We investigate some relation between exact triangle of polydules and variety of polydules.
We study varieties of complexes of projective modules with fixed ranks, and relate these varieties to the varieties of their homologies. We show that for an algebra of global dimension at most two, these two varieties are related by a pair of morphisms which are smooth with irreducible fibers.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.