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 (Rhipicephalus appendiculatus) with its hosts. Such models are rare due to the complexity and lack of information on the entire stages of ticks life cycles. Most models are simulations rather than analytical. The vector is categorized into a discrete number of compartments according to its life cycle. The starting model in this article consists of a system of differential equations with constant coefficients. A general model on a stage structured population with unlimited host density is developed. From the characteristic polynomial of the system a sensitivity analysis for the population parameters is carried out in detail. The model is then improved by incorporating host abundance and availability. This is done on the basis of a demand-driven and ratio-dependent functional response model. The improved model adequately represents the dynamics of a stage-structured vector population under conditions of varying host density. The model allows the qualitative evaluation of several management strategies and is expected to guide future research work.