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. 2022 Sep:351:108885.
doi: 10.1016/j.mbs.2022.108885. Epub 2022 Jul 27.

Minimising the use of costly control measures in an epidemic elimination strategy: A simple mathematical model

Michael J Plank  1
Affiliations

Minimising the use of costly control measures in an epidemic elimination strategy: A simple mathematical model

Michael J Plank. Math Biosci. 2022 Sep.

Abstract

Countries such as New Zealand, Australia and Taiwan responded to the Covid-19 pandemic with an elimination strategy. This involves a combination of strict border controls with a rapid and effective response to eliminate border-related re-introductions. An important question for decision makers is, when there is a new re-introduction, what is the right threshold at which to implement strict control measures designed to reduce the effective reproduction number below 1. Since it is likely that there will be multiple re-introductions, responding at too low a threshold may mean repeatedly implementing controls unnecessarily for outbreaks that would self-eliminate even without control measures. On the other hand, waiting for too high a threshold to be reached creates a risk that controls will be needed for a longer period of time, or may completely fail to contain the outbreak. Here, we use a highly idealised branching process model of small border-related outbreaks to address this question. We identify important factors that affect the choice of threshold in order to minimise the expect time period for which control measures are in force. We find that the optimal threshold for introducing controls decreases with the effective reproduction number, and increases with overdispersion of the offspring distribution and with the effectiveness of control measures. Our results are not intended as a quantitative decision-making algorithm. However, they may help decision makers understand when a wait-and-see approach is likely to be preferable over an immediate response.

Keywords: Branching process; Epidemiological modelling; Infectious disease modelling; Public health.

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Conflict of interest statement

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Figures

Fig. 1
Fig. 1
(a) Expected number of generations of the branching process spent under control measures for different values of the reproduction number in the controlled phase Rc, and (b) probability that the control trigger is met (i.e. that control measures are introduced before the outbreak is eliminated), as a function of the chosen control trigger. Reproduction number in the uncontrolled phase R0=1.6 and dispersion parameter κ=0.25.
Fig. 2
Fig. 2
Optimal trigger k for implementing control measures for combinations of the reproduction number in the uncontrolled and controlled phases and for three values of the offspring distribution dispersion parameter κ. Smaller values of κ correspond to more variance in the offspring distribution. Note different y-axis scales in (c,d) compared to (a,b).
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