Optimal control of dengue epidemic outbreaks under limited resources

In this paper, we reflect upon control intervention practices habitually exerted by healthcare authorities in tropical areas that suffer from incidental outbreaks of dengue fever, in particular, the city of Cali, Colombia. Such control interventions, principally based on the insecticide spraying, are carried out sporadically in order to overcome an ongoing epidemic or at least to reduce its size. It is worth pointing out that control actions of this type do not usually account for sufficient budget because epidemic outbreaks are difficult to predict. In practical terms, these occasional control interventions are performed by spraying, as quickly as possible, all existing stock of insecticide (regardless of its lethality) and employing all available manpower. The goal of this paper is to design better strategies for insecticide-based control actions, which are capable of preventing more human infections at no additional cost, and to reveal the obsolescence of current vector eradication practices. Our approach relies on dynamic optimization, where the number of averted human infections is maximized under budget constraint and subject to a simple dengue transmission model amended with one control variable that stands for the insecticide spraying. As a result, we obtain structurally robust control intervention policies that demonstrate better performance and higher resilience to possible budget limitations than traditional modus operandi.