Abstract
BackgroundMass drug administration (MDA) has been proposed as an intervention to achieve local extinction of malaria. Although its effect on the reproduction number is short lived, extinction may subsequently occur in a small population due to stochastic fluctuations. This paper examines how the probability of stochastic extinction depends on population size, MDA coverage and the reproduction number under control, Rc. A simple compartmental model is developed which is used to compute the probability of extinction using probability generating functions. The expected time to extinction in small populations after MDA for various scenarios in this model is calculated analytically.ResultsThe results indicate that mass drug administration (Firstly, Rc must be sustained at Rc < 1.2 to avoid the rapid re-establishment of infections in the population. Secondly, the MDA must produce effective cure rates of >95% to have a non-negligible probability of successful elimination. Stochastic fluctuations only significantly affect the probability of extinction in populations of about 1000 individuals or less. The expected time to extinction via stochastic fluctuation is less than 10 years only in populations less than about 150 individuals. Clustering of secondary infections and of MDA distribution both contribute positively to the potential probability of success, indicating that MDA would most effectively be administered at the household level.ConclusionsThere are very limited circumstances in which MDA will lead to local malaria elimination with a substantial probability.
Highlights
Mass drug administration (MDA) has been proposed as an intervention to achieve local extinction of malaria
At an MDA coverage of 95% (Fig. 1, marked in red), which is only achievable in interventions with excellent operational characteristics, the probability of elimination is negligible in populations over 1000 or where Rc is greater than 1.2
In the case where secondary cases result homogeneously from primary cases but MDA coverage is clustered, the model predicts a higher probability of elimination as the clustering in MDA coverage increases (Fig. 2)
Summary
Mass drug administration (MDA) has been proposed as an intervention to achieve local extinction of malaria. Its effect on the reproduction number is short lived, extinction may subsequently occur in a small population due to stochastic fluctuations. Mass drug administration (MDA) is one additional intervention that has been proposed as a key to eliminating the residual transmission. Mathematical models of the impact of MDA against malaria transmission agree that without some other sustained change, such as improved vector control, the effects of MDA on prevalence are likely to be transient [9]. The possibility of elimination of malaria by MDA on islands arises because extinction is a stochastic event that can occur in a small pathogen population even if the prevailing reproduction number under control is greater than unity
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