Modelling the control strategies against dengue in Singapore

Abstract

Notified 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.

Fig. 1

Map of Singapore showing the 2005 dengue outbreak. ■, Aedes albopictus-infested area; , Aedes aegypti-infested area; , dengue cases (from reference [7]).

Fig. 2

Correlation between the ambient temperature and dengue cases in the last 17 years (data from reference [7]).

Fig. 3

Fitting accuracy of model (1) to real data for years 2003, 2004 and 2005 (data from http://www.moh.gov.sg/cmaweb/attachments/publication).

Fig. 4

Simulation of the projected number of cases if the control programme was not introduced in October 2005, compared with real data (from http://www.moh.gov.sg/cmaweb/attachments/publication).

Fig. 5

Simulation of the impact of continuous pure strategies at the level of 10%, i.e. increasing mosquito mortality rate by 10% (adulticide; · · · · · · ·), increasing immature-stage mortality rate by 10% (larvicide; - - - -), and decreasing the probability of effective contagiousness between infected humans and mosquitoes by 10% (quarantine; ––––). Note that adulticide is the most effective strategy.

Fig. 6

Simulation of the impact of a mixed strategy (––––) consisting of the combination of a 5% increase in mosquito mortality rate (· · · · · · · · ·) and a 10% increase in immature-stages mortality rate (- - - -) compared with pure strategies. Note that the combination is more effective than each pure strategy.

Fig. 7

Simulation of six pulses of discrete control for three pure strategies, namely, reducing 50% of the mosquito population (· · · · · · · · ·), reducing 50% of immature stages (eggs, - - - -), and destroying breeding places by reducing the immature stages' carrying capacity by 50% (K_S, –––), compared with no control (). Note that none of the strategies if applied in isolation explain the real data (◆).

Fig. 8

Simulation of a mixed strategy combining the three strategies described in Figure 7. Note that this combination reproduces the actual descendent trend of the data.

Fig. 9

Simulation of the actual control strategy applied in Singapore from October, 2005, compared to the real data (see text for a description of the strategy).

Fig. 10

Simulation of the model by Newton & Reiter [15] showing that the impact on the number of mosquitoes by a single pulse of fogging is ephemeral.

Fig. 11

Simulation of model (1) with the same condition as used by Newton & Reiter [15] (four weekly fogging applications). Note that in our model the impact of this strategy is more durable.