Chasing up and locking down the virus: Optimal pandemic interventions within a network

Abstract

During the COVID-19 pandemic countries invested significant amounts of resources into its containment. In early stages of the pandemic most of the (nonpharmaceutical) interventions can be classified into two groups: (i) testing and identification of infected individuals, (ii) social distancing measures to reduce the transmission probabilities. Furthermore, both groups of measures may, in principle, be targeted at certain subgroups of a networked population. To study such a problem, we propose an extension of the SIR model with additional compartments for quarantine and different courses of the disease across several network nodes. We develop the structure of the optimal allocation and study a numerical example of three symmetric regions that are subject to an asymmetric progression of the disease (starting from an initial hotspot). Key findings include that (i) for our calibrations policies are chosen in a "flattening-the-curve," avoiding hospital congestion; (ii) policies shift from containing spillovers from the hotspot initially to establishing a symmetric pattern of the disease; and (iii) testing that can be effectively targeted allows to reduce substantially the duration of the disease, hospital congestion and the total cost, both in terms of lives lost and economic costs.

Figure 1

Flow chart of the SIR‐type model. Gray boxes: compartments, gray ellipses: controls, black arrows: flows between the compartments, dashed arrows: flows that can be changed by controls.

Figure 2

Original and final smoothed version of the mortality function describing congestion in the health sector.

Figure 3

Pandemic development for the “Uncontrolled” case.

Figure 4

Comparison of the pandemic development for the “No testing,” “Ineffective testing,” and “Effective testing” case.

Figure 5

Optimal target transmission rates for the “No testing,” “Ineffective testing,” and “Effective testing” case.

Figure 6

Optimal testing strategy in the “ineffective” and “effective” testing case.

Figure 7

Origins of costs for the “No testing” (left), “Ineffective testing” (middle) and “Effective testing” case (right).