Optimal control of dengue epidemic outbreaks under limited resources

Abstract

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 insecticidebased 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. K E Y W O R D Sdengue outbreaks, insecticide-based vector control, isoperimetric constraint, optimal control, optimization, Ross-Macdonald model Stud Appl Math. 2020;144:185-212.wileyonlinelibrary.com/journal/sapm

Dengue infection modeling and its optimal control analysis in East Java, Indonesia

“…8 (f), it can be seen that the insecticide is maintained at full effort for 72 days before drastically reduces for the rest of the intervention. These results seem to be consistent with previous research [36] , [42] which found that the insecticide spraying alone had the effect of rapidly reducing the number of infectious humans, almost enabling eradication of disease.

Figure 8 Numerical results of the model using insecticide only.

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“…The use of the control for dengue infection as a prevention only has been considered in the work [33] , [41] . The control insecticide spraying only has been considered in dengue control model given in [42] . The use of both the control for dengue control in the population is considered in [36] , [43] .…”

Optimal vaccination strategy for dengue transmission in Kupang city, Indonesia

“…In optimal control approach, we use quadratic terms in the control variables to capture the nonlinear cost in the implementation of controls. This approach is rather conventional and has been frequently used in the epidemiological modelling including dengue modelling [11,13,26 approach to investigate the effects of vector control and vaccination on dengue transmission dynamics. They used quadratic terms in the control variables as to represent the nonlinear cost [23], which has been also used in the other work for the similar reason to investigate the dengue transmission dynamics in the presence of controls [11,13,26,15,23,39,40,12].…”

“…In optimal control approach, we use quadratic terms in the control variables to capture the nonlinear cost in the implementation of controls. This approach is rather conventional and has been frequently used in the epidemiological modelling including dengue modelling [11] , [13] , [26] , [15] , [23] , [39] , [40] , [12] . Rawson et al implemented optimal control approach to investigate the effects of vector control and vaccination on dengue transmission dynamics.…”

“…It is generally believed that there is no linear relationship between effects of intervention and the cost of intervention [23] , [11] and hence the quadratic costs have been commonly used [11] , [13] , [23] , [24] , [25] , [26] . This approach is rather conventional in the optimal control problems of the epidemiological modelling and this simplifies the mathematical analysis [23] , [26] . The use of linear term in the cost function leads to bang-bang control [23] , [27] , [28] .…”