Munyinyi, David Mbuthia; (2003) Non-linear dynamics of trophic interactions between disease vectors and herbivore hosts: Part I: Migrant vectors (tsetse flies). Part II: Non-migrant vectors (tri-phasic ticks). Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis has two parts. Part I models the feeding and movement behaviour of tsetse fly species Glossina as a "migrant" disease vector in relation to cattle, plants and chemo-attractants using reaction-diffusion equations that yields the 'Interaction Diffusion Equations' (IDE) that models the fly's trophic interactions. Through its feeding behavior, tsetse transmits trypanosorne parasites that cause the disease trypanosomiasis. Analysis of the IDE system is restricted to a 1-dimensional patchy environment with and without traps. The impact of trapping as 'killer-hosts' on the fly population, with conditions for efficient tsetse traps and suppression of tsetse populations is presented. Part II models the effects of the tri-phasic tick Rhipicephalus appendiculatus as a "non-migrant" disease vector which transmits micro-parasites that cause the disease theileriosis. Tick population is modelled at "parasitic" and "'free-living" phases of its life-cycle using systems of non-linear ordinary differential equations. Model equilibria are analyzed both with and without an active host immune response, to elucidate necessary conditions for take-off or suppression of tick population. Various cases of host immune response to on-host tick load are considered. Results from Part I show that factors that measures trap efficiency contain all the information needed to specify the conditions required to lower fly population through trapping. Two measures based on fly-trap parameters are obtained, the 'actual' and 'required' trap efficiency. We show that whenever the 'actual' is greater than the 'required', trap is efficient enough to cause the added trap induced fly mortality to be so large that the fly population is eventually reduced. From Part II, measure of 'zebu content' that quantifies herd resistance to ticks is derived from either "parasitic" tick loads or quantity of egg mass laid by engorged "free-living" females. We show that having resistance animals is necessary but not sufficient to lower tick population. The sufficient condition is whenever 'zebu content' is lower than one when sufficient numbers of resistance cattle are present so that herd resistance is high, leading to the collapse of tick population. It is also shown that the population of "free-living" ticks collapses whenever the overall tick 'cost of feeding' index computed from egg mass is below the threshold value. Results from computer simulations and areas for further improvements and research are presented.

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