A cross-linking model for the activation of the A cell or immune accessory cell as a function of certain extracellular conditions is developed to determine the valency of the specific factor receptor on the A cell surface. It is found that such a determination can be made based on the FWHM of cross-linking curves which differ by a full order of magnitude between the bivalent receptor case and the monovalent receptor case. This determination can be made provided one can obtain accurate values for the equilibrium constants which characterize the system and provided that activation and IL-1 secretion is a linear function of cross-linking. It is also found that a determination of valence can be made if the equilibrium constants are such that substantial one receptor bridge formation takes place (one antibody molecule bound on both ends by the same receptor). This one-receptor bridge formation only takes place if the receptor is bivalent, and it presents itself in the cross-linking curve in a very distinctive manner. A second network model described as an ecological competition model of steady state lymphocyte populations is presented. This model, known as the symmetrical network theory is analysed numerically by integration of the differential equations and shown to provide a reasonable qualitative picture of the immune system's stable steady states, and offer a glimpse of state switching. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The effect of the inclusion of sexual behaviour, particularly three sexual orientation classes, on the transmission dynamics of HPV and cervical cancer incidence was investigated. A comprehensive literature review of mathematical models of HPV transmission and the natural history of cervical cancer was concluded. A mathematical model using ordinary differential equations was developed, which incorporated the three sexual orientation classes, and a sexual mixing algorithm for modelling the transmission dynamics. Reproduction numbers, determined through a simplified version of the developed model, indicated that the bisexual population could form a bridge between the heterosexual and homosexual population. The level of interaction is determined by the selection preferences of a bisexual individual to form a partnership with an individual of the same or opposite sex. The model was simulated, with parameters based on a South African population and HPV type 16/18, to investigate the effects of HIV status, sexual orientation and various vaccination strategies on HPV transmission and cervical cancer incidence. The results indicated that HIV status is a significant factor when determining cervical cancer incidence. The results regarding vaccination strategies agreed with results from the literature review with a two sex before sexual debut and catch up program the most effective, noting that with increased vaccination coverage of females the marginal impact on cervical cancer incidence of this approach diminished.