Article Contents
Article Contents

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

• * Corresponding author: Caterina Scoglio
• 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.

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

 Citation:

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

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

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

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.

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.

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.

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

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 ($\gamma$) $0.33$

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 ($\eta_H$) $0.005$
•  C. Browne , H. Gulbudak  and  G. Webb , Modeling contact tracing in outbreaks with application to Ebola, Journal of Theoretical Biology, 384 (2015) , 33-49.  doi: 10.1016/j.jtbi.2015.08.004. G. Chowell  and  C. Viboud , Is it growing exponentially fast?-Impact of assuming exponential growth for characterizing and forecasting epidemics with initial near-exponential growth dynamics, Infectious Disease Modelling, 1 (2016) , 71-78.  doi: 10.1016/j.idm.2016.07.004. O. Diekmann , J. A. P. Heesterbeek  and  J. A. J. Metz , On the definition and the computation of the basic reproduction ratio $R_{0}$ in models for infectious diseases in heterogeneous populations, Journal of Mathematical Biology, 28 (1990) , 365-382.  doi: 10.1007/BF00178324. M. G. Dixon  and  I. J. Schafer , Ebola Viral Disease Outbreak - West Africa, 2014, MMWR Morb Mortal Wkly Rep, 63 (2014) , 548-551. K. T. Eames  and  M. J. Keeling , Contact tracing and disease control, Proceedings of the Royal Society of London B: Biological Sciences, 270 (2003) , 2565-2571.  doi: 10.1098/rspb.2003.2554. F. O. Fasina, A. Shittu, D. Lazarus, O. Tomori, L. Simonsen, C. Viboud and G. Chowell, Transmission dynamics and control of Ebola virus disease outbreak in Nigeria, July to September 2014, Eurosurveillance, 19 (2014), 20920. doi: 10.2807/1560-7917.ES2014.19.40.20920. M. Greiner , D. Pfeiffer  and  R. D. Smith , Principles and practical application of the receiver-operating characteristic analysis for diagnostic tests, Preventive Veterinary Medicine, 45 (2000) , 23-41.  doi: 10.1016/S0167-5877(00)00115-X. J. M. Heffernan , R. J. Smith  and  L. M. Wahl , Perspectives on the basic reproductive ratio, Journal of the Royal Society Interface, 2 (2005) , 281-293.  doi: 10.1098/rsif.2005.0042. M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals, Princeton University Press, Princeton, NJ, 2008. I. Z. Kiss , D. M. Green  and  R. R. Kao , Disease contact tracing in random and clustered networks, Proceedings of the Royal Society of London B: Biological Sciences, 272 (2005) , 1407-1414.  doi: 10.1098/rspb.2005.3092. D. Klinkenberg , C. Fraser  and  H. Heesterbeek , The effectiveness of contact tracing in emerging epidemics, PloS One, 1 (2006) , e12.  doi: 10.1371/journal.pone.0000012. S. Liu , N. Perra , M. Karsai  and  A. Vespignani , Controlling contagion processes in activity driven networks, Physical review letters, 112 (2014) , 118702.  doi: 10.1103/PhysRevLett.112.118702. A. S. da Mata and R. Pastor-Satorras, Slow relaxation dynamics and aging in random walks on activity driven temporal networks, The European Physical Journal B, 88 (2015), Art. 38, 8 pp. doi: 10.1140/epjb/e2014-50801-1. N. Perra, B. Gonçalves, R. Pastor-Satorras and A. Vespignani, Activity Driven Modeling of Time Varying Networks, Scientific Reports, 2012. doi: 10.1038/srep00469. N. Perra , A. Baronchelli , D. Mocanu , B. Gonc'calves , R. Pastor-Satorras  and  A. Vespignani , Random walks and search in time-varying networks, Physical review letters, 109 (2012) , 238701.  doi: 10.1103/PhysRevLett.109.238701. A. Rizzo , B. Pedalino  and  M. Porfiri , A network model for Ebola spreading, Journal of theoretical biology, 394 (2016) , 212-222.  doi: 10.1016/j.jtbi.2016.01.015. A. Rizzo , M. Frasca  and  M. Porfiri , Effect of individual behavior on epidemic spreading in activity-driven networks, Physical Review E, 90 (2014) , 042801.  doi: 10.1103/PhysRevE.90.042801. A. Rizzo and M. Porfiri, Toward a realistic modeling of epidemic spreading with activity driven networks, in Temporal Network Epidemiology (N. Masuda and P. Holme), Springer, (2017), 317-319. N. M. Shahtori , C. Scoglio , A. Pourhabib  and  F. D. Sahneh , Sequential Monte Carlo filtering estimation of Ebola progression in West Africa, American Control Conference(ACC), (2016) , 1277-1282.  doi: 10.1109/ACC.2016.7525093. M. D. Shirley  and  S. P. Rushton , The impacts of network topology on disease spread, Ecological Complexity, 2 (2005) , 287-299.  doi: 10.1016/j.ecocom.2005.04.005. F. Shuaib , R. Gunnala , E. O. Musa , F. J. Mahoney , O. Oguntimehin , P. M. Nguku , S. B. Nyanti , N. Knight , N. S. Gwarzo , O. Idigbe , A. Nasidi  and  J. F. Vertefeuille , Ebola virus disease outbreak-Nigeria, July-September 2014, MMWR Morb Mortal Wkly Rep, 63 (2014) , 867-872. M. Starnini  and  R. Pastor-Satorras , Temporal percolation in activity-driven networks, Physical Review E, 89 (2014) , 032807.  doi: 10.1103/PhysRevE.89.032807. M. Starnini  and  R. Pastor-Satorras , Topological properties of a time-integrated activity-driven network, Physical Review E, 87 (2013) , 062807.  doi: 10.1103/PhysRevE.87.062807. K. Sun, A. Baronchelli and N. Perra, Contrasting effects of strong ties on SIR and SIS processes in temporal networks, The European Physical Journal B, 88 (2015), Art. 326, 8 pp. doi: 10.1140/epjb/e2015-60568-4. L. Zino , A. Rizzo  and  M. Porfiri , Continuous-Time Discrete-Distribution Theory for Activity-Driven Networks, Physical Review Letters, 117 (2016) , 228302.  doi: 10.1103/PhysRevLett.117.228302. Cases of Ebola Diagnosed in the United States, 2014. Available from: https://www.cdc.gov/vhf/ebola/outbreaks/2014-west-africa/united-states-imported-case.html. Implementation and Management of Contact Tracing for Ebola Virus Disease, Emergency Guideline by the World Health Organization, 2015. Available from: https://www.cdc.gov/vhf/ebola/pdf/contact-tracing-guidelines.pdf.

Figures(7)

Tables(2)