Ticks and tick-borne diseases: a vector-host interaction model for the brown ear tick (Rhipicephalus appendiculatus)

An analytical model is derived for the interaction of the brown ear tick (R hipicephalus appendiculatus) with its hosts. Such models are rare due to th e complexity and lack of information on the entire stages of ticks life cyc les. Most models are simulations rather than analytical. The vector is cate gorized into a discrete number of compartments according to its life cycle. The starting model in this article consists of a system of differential eq uations with constant coefficients. A general model on a stage structured p opulation with unlimited host density is developed. From the characteristic polynomial of the system a sensitivity analysis for the population paramet ers is carried out in detail. The model is then improved by incorporating h ost abundance and availability. This is done on the basis of a demand-drive n and ratio-dependent functional response model. The improved model adequat ely represents the dynamics of a stage-structured vector population under c onditions of varying host density. The model allows the qualitative evaluat ion of several management strategies and is expected to guide future resear ch work.