A stochastic model for the probability of malaria extinction by mass drug administration

Background: Mass 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, R-c. 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. Results: The results indicate that mass drug administration (Firstly, R-c must be sustained at R-c < 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. Conclusions: There are very limited circumstances in which MDA will lead to local malaria elimination with a substantial probability.