Dedekind order completion of C(X) by Hausdorff continuous functions

The concept of Hausdorff continuous interval valued functions, developed within the theory of Hausdorff approximations and originaly defined for interval valued functions of one real variable is extended to interval valued functions defined on a topological space X. The main result is that the set of all finite Hausdorff continuous functions on any topological space X is Dedekind order complete. Hence it contains the Dedekind order completion of the set C(X) of all continuous real functions defined on X as well as the Dedekind order completion of the set C_b(X) of all bounded continuous functions on X. Under some general assumptions about the topological space X the Dedekind order completions of both C(X) and C_b(X) are characterised as subsets of the set of all Hausdorff continuous functions. This solves a long outstanding open problem about the Dedekind order completion of C(X). In addition, it has major applications to the regularity of solutions of large classes of nonlinear PDEs

Sterile insect technology for control of Anopheles mosquito: a mathematical feasibility study

Anopheles mosquito is a vector responsible for the transmission of diseases like Malaria which a_ect many people. Hence its control is a major prevention strategy. Sterile Insect Technology (SIT) is a nonpolluting method of insect control that relies on the release of sterile males. Mating of the released sterile males with wild females leads to non hatching eggs. Thus, if sterile males are released in su_cient numbers or over a su_cient period of time, it can leads to the local reduction or elimination of the wild population. We study the e_ectiveness of the application of SIT for control of Anopheles mosquito via mathematical modeling. Our main result is that there exists a threshold release rate ^_ depending only on the basic o_spring number R and the wild mosquito equilibrium for males such that a release rate higher than ^_ results in elimination of the mosquito population irrespective of its initial size. A release rate _ which is lower than ^_ eliminates the mosquito populations only if it is su_ciently small. If the population is at the wild equilibrium it is reduced by a percentage depending on _ and R only. (Résumé d'auteur