Modelling triatomine bug population and Trypanosoma rangeli transmission dynamics: Co-feeding, pathogenic effect and linkage with chagas disease.

Trypanosoma rangeli (T. rangeli), a parasite, is not pathogenic to human but pathogenic to some vector species to induce the behavior changes of infected vectors and subsequently impact the transmission dynamics of other diseases such as Chagas disease which shares the same vector species. Here we develop a mathematical model and conduct qualitative analysis for the transmission dynamics of T. rangeli. We incorporate both systemic and co-feeding transmission routes, and account for the pathogenic effect using infection-induced fecundity and fertility change of the triatomine bugs. We derive two thresholds R (the triatomine bug basic reproduction number) and R (the T. rangeli basic reproduction number) to delineate the dynamical behaviors of the ecological and epidemiological systems. We show that when R>1 and R>1, a unique parasite positive equilibrium E* appears. We find that E* can be unstable and periodic oscillations can be observed where the pathogenic effect plays a significant role. Implications of the qualitative analysis and numerical simulations suggest the need of an integrative vector-borne disease prevention and control strategy when multiple vector-borne diseases are transmitted by the same set of vector species.