Quantifying the impact of early-stage contact tracing on controlling Ebola diffusion

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doi:10.3934/mbe.2018053

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2018, Volume 15, Issue 5: 1165-1180. Doi: 10.3934/mbe.2018053

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Quantifying the impact of early-stage contact tracing on controlling Ebola diffusion

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Department of Electrical and Computer Engineering, Kansas State University, Manhattan, KS 66506, USA

* Corresponding author: Caterina Scoglio
* Corresponding author: Caterina Scoglio

Received: September 14, 2017

Revised: January 26, 2018

Published: September 2018

This article is based on work supported by the National Science Foundation grants SCH-1513639 and CIF-1423411

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Abstract

Recent experience of the Ebola outbreak in 2014 highlighted the importance of immediate response measure to impede transmission in the early stage. To this aim, efficient and effective allocation of limited resources is crucial. Among the standard interventions is the practice of following up with the recent physical contacts of the infected individuals -- known as contact tracing. In an effort to understand the effects of contact tracing protocols objectively, we explicitly develop a model of Ebola transmission incorporating contact tracing. Our modeling framework is individual-based, patient-centric, stochastic and parameterizable to suit early-stage Ebola transmission. Notably, we propose an activity driven network approach to contact tracing, and estimate the basic reproductive ratio of the epidemic growth in different scenarios. Exhaustive simulation experiments suggest that early contact tracing paired with rapid hospitalization can effectively impede the epidemic growth. Resource allocation needs to be carefully planned to enable early detection of the contacts and rapid hospitalization of the infected people.

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Mathematics Subject Classification: Primary: 92B05, 68U20; Secondary: 65C20.

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Figure 1. Schematic of the transition processes in the Ebola progression with contact tracing model.

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Figure 2. The epidemic attack ratio as a function of $\alpha^{-1}$. The results are the averages of $10,000$ simulations.

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Figure 3. The epidemic attack ratio as a function of $\gamma^{-1}$. The results are the averages of $10,000$ simulations.

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Figure 4. 3-D $ROC$ curve of contact tracing with $5$ identification delay implemented in three different scenarios. The results are the averages of $10,000$ simulations.

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Figure 5. 2-D $ROC$ curve of contact tracing implementation in three different scenarios. The area under the curve (AUC) values for contact tracing starting on day 1, day 9 and day 22 are respectively 0.6550, 0.4060 and 0.1207. The results are the averages of $10,000$ simulations.

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Figure 6. $R_0$ as a function of the identification delay, $\alpha^{-1}$ in three scenarios. The results are the averages of $10,000$ simulations.

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Figure 7. $R_0$ as a function of the hospitalization delay, $\gamma^{-1}$. The results are the averages of $10,000$ simulations.

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Table 1. Time-invariant parameters of Ebola contagion process

Parameter	Value
Transmission probability($\beta$)	$0.11$
Incubation rate ($\lambda$)	$0.095$
Recovery/removal probability ($\delta$)	$0.1$
Hospitalization probability in existence of contact tracing ($\gamma_T$)	$0.9$
Hospitalization probability ($\gamma$)	$0.33$

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Table 2. Parameters of activity driven network generator

Parameter	Value
Density function exponent ($c$)	$2.2$
Links per active node ($m$)	$7$
Scaling factor for susceptible ($\eta_S$)	$2.2$
Scaling factor for infected ($\eta_I$)	$1.1$
Scaling factor for hospitalized ($\eta_H$)	$0.005$

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