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A critical review of some current malaria models is given in which a new model of superinfection is presented. An alternative malaria model, partly stochastic and party deterministic, is then proposed and results of the simulation of the model are discussed. Simplified versions of the model are used to analyse longitudinal survey data from a World Health Organization malaria project, carried out in Northern Nigeria.

Many differential geometric concepts such as (isometric) immersion, stability, etc., realized in Euclidean spaces proved to be also realized in manifolds without conjugate points while other concepts are found to be strictly associated with Euclidean spaces. In fact, this thesis may be considered as a trial for finding out to what extent geometric phenomena in Euclidean spaces are still l valid in manifolds without conjugate points. In the introduction, we have quoted the necessary background material for the following chapters. Specially, we have concentrated on the geometry of submanifolds. The interesting problem of rigidity of submanifolds lies in three different categories : finite rigidity, continuous rigidity and infinitesimal rigidity. These three types of rigidity have been studied in hyperbolic spaces in chapter I, sections 1 and 2. K. Nomizu, B. Snmyth (1969) and S. Braidi, C.C. Hsuing (1970) studied some geometric properties of immersed submanifolds in Euclidean sphere essentially the behaviour of the second fundamental form and the Gauss map. In chapter II (sections 1, 2) we have carried out similar study for immersed submanifolds in hyperbolic spaces which shows some deviations from the corresponding one in Euclidean sphere. Since B.Y. Chen's paper (1973) which established the geometric concept of stability of submanifolds in Euclidean spaces, other geometers tried to extend this concept to non-Euclidean spaces. In chapter II (section 3) we share this development through studying stability of surfaces in hyperbolic 3-dimensional space. The most interesting part of our thesis is the last chapter which deals with tight and taut (convex-minimal) immersions in manifolds without conjugate points. Some geometric concepts such as (spherical) two-piece property, h-two-piece property, total (absolute) curvature,... e t c . , have been introduced. Relations between the above concepts have been adopted. We expect for this part to receive more attention in the future to discover more results and to generalize other Euclidean concepts which we did not touch.

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In this thesis work is described that arose out of a study of harmonic Riemannian manifolds. A definition of harmonicity is given and from this it is shown how the Ledger conditions on the curvature of a harmonic manifold may be derived in principle and the first four are written down. The first three Ledger conditions are put into local co-ordinate form and simpler conditions are derived, the most important being the super-Einstein condition. The idea of the Schur property is also introduced. The mean-value work of Gray and Willmore is described and extended as far as the r(^8) term under some simplifying conditions. Finally there is an investigation of the extent to which the compact classical simple Lie groups with bi-invariant metrics can satisfy Ledger’s first three conditions.

The purpose of this research is the utilization of experimental structure function moments to test various models of the quark energy-momentum distribution inside the nucleon and to extend these models to discussion in a wider context: the contemporary interacting field theory of quarks and gluons (Quantum Chromodynamics - QCP); and static properties of the nucleon. A complete connection between a general quark energy-momentum distribution and the structure function moments is presented and a cure for the pathology of the lack of necessary kinematical restrictions in these models is extensively validated.

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