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SUMMARYNotified cases of dengue infections in Singapore reached historical highs in 2004 (9459 cases) and 2005 (13 817 cases) and the reason for such an increase is still to be established. We apply a mathematical model for dengue infection that takes into account the seasonal variation in incidence, characteristic of dengue fever, and which mimics the 2004-2005 epidemics in Singapore. We simulated a set of possible control strategies and confirmed the intuitive belief that killing adult mosquitoes is the most effective strategy to control an ongoing epidemic. On the other hand, the control of immature forms was very efficient in preventing the resurgence of dengue epidemics. Since the control of immature forms allows the reduction of adulticide, it seems that the best strategy is to combine both adulticide and larvicide control measures during an outbreak, followed by the maintenance of larvicide methods after the epidemic has subsided. In addition, the model showed that the mixed strategy of adulticide and larvicide methods introduced by the government seems to be very effective in reducing the number of cases in the first weeks after the start of control.

Yellow fever and dengue are viral infections that in urban centres are transmitted by the same arthropod vector, a mosquito of the genus Aedes. In order to estimate the risk of an epidemic of urban yellow fever in a dengue-infested area we calculated the threshold in the basic reproduction number, R0, of dengue, above which any single sylvatic yellow fever-infected individual will trigger an urban yellow fever epidemic. Specifically, we analysed the relationship between the extrinsic incubation period and the duration of viraemia, from which it is possible to define the R0 for dengue that would also suggest an outbreak potential for yellow fever. We also calculated the critical proportion of people to vaccinate against yellow fever in order to prevent an epidemic in a dengue-endemic area. The theory proposed is illustrated by the case of São Paulo State in southern Brazil, where dengue is endemic and the risk of urban yellow fever is already imminent.

To construct a self-adjoint operator the domain of the operator has to be specified by imposing an appropriate boundary condition or conditions on the wave functions on which the operator acts. We illustrate situations for which different boundary conditions lead to different operators and hence to different physics.

SummaryThe magnitude of the basic reproduction ratio R 0 of an epidemic can be estimated in several ways, namely, from the final size of the epidemic, from the average age at first infection, or from the initial growth phase of the outbreak. In this paper, we discuss this last method for estimating R 0 for vectorborne infections. Implicit in these models is the assumption that there is an exponential phase of the outbreaks, which implies that in all cases R 0 > 1. We demonstrate that an outbreak is possible, even in cases where R 0 is less than one, provided that the vector-to-human component of R 0 is greater than one and that a certain number of infected vectors are introduced into the affected population. This theory is applied to two real epidemiological dengue situations in the southeastern part of Brazil, one where R 0 is less than one, and other one where R 0 is greater than one. In both cases, the model mirrors the real situations with reasonable accuracy.keywords basic reproduction number, epidemiology, mathematical models, vector-borne infections, dengue fever