Transmission dynamics of a chagas disease model with standard incidence infection


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In this paper, an insect-parasite-host model with Ricker's type re-production of triatomines and the standard incidence rate of the interaction between insects and hosts is formulated to study the transmission dynamics of Chagas disease. Two thresholds of the ecological basic reproduction number of triatomines and the epidemiological basic reproduction number of Chagas disease are derived, which determine the dynamics of this model. As a result, the existence of equilibria and the local/global stabilities of the equilibrium are accordingly obtained. Moreover, backward bifurcation, forward bifurca-tion and saddle-node bifurcation are also shown analytically and numerically. Biologically speaking, Chagas disease may undergo outbreak if the number of bites of per triatomine bug per unit time or the transmission probability from infected bugs to susceptible competent hosts per bite increase.
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Key words
Chagas disease,Ricker's type reproduction,standard incidence rate,backward/forward bifurcation
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