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In this work, we use a mathematical model for dengue transmission with the aim of analysing and comparing two dengue epidemics that occurred in Salvador, Brazil, in 1995-1996and 2002. Using real data, we obtain the force of infection, L, and the basic reproductive number, R 0 , for both epidemics. We also obtain the time evolution of the effective reproduction number, R(t), which results in a very suitable measure to compare the patterns of both epidemics. Based on the analysis of the behaviour of R 0 and R(t) in relation to the adult mosquito control parameter of the model, we show that the control applied only to the adult stage of the mosquito population is not sufficient to stop dengue transmission, emphasizing the importance of applying the control to the aquatic phase of the mosquito.

A model for the transmission of dengue fever with variable human population size is analyzed. We find three threshold parameters which govern the existence of the endemic proportion equilibrium, the increase of the human population size, and the behaviour of the total number of human infectives. We prove the global asymptotic stability of the equilibrium points using the theory of competitive systems, compound matrices, and the center manifold theorem.

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