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October  2018, 15(5): 1165-1180. doi: 10.3934/mbe.2018053

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

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

* Corresponding author: Caterina Scoglio

Received  September 15, 2017 Revised  January 27, 2018 Published  May 2018

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

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.

Citation: Narges Montazeri Shahtori, Tanvir Ferdousi, Caterina Scoglio, Faryad Darabi Sahneh. Quantifying the impact of early-stage contact tracing on controlling Ebola diffusion. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1165-1180. doi: 10.3934/mbe.2018053
References:
[1]

C. BrowneH. 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.  Google Scholar

[2]

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.  Google Scholar

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O. DiekmannJ. 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.  Google Scholar

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M. G. Dixon and I. J. Schafer, Ebola Viral Disease Outbreak - West Africa, 2014, MMWR Morb Mortal Wkly Rep, 63 (2014), 548-551.   Google Scholar

[5]

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.  Google Scholar

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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.  Google Scholar

[7]

M. GreinerD. 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.  Google Scholar

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J. M. HeffernanR. 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.  Google Scholar

[9]

M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals, Princeton University Press, Princeton, NJ, 2008.  Google Scholar

[10]

I. Z. KissD. 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.  Google Scholar

[11]

D. KlinkenbergC. Fraser and H. Heesterbeek, The effectiveness of contact tracing in emerging epidemics, PloS One, 1 (2006), e12.  doi: 10.1371/journal.pone.0000012.  Google Scholar

[12]

S. LiuN. PerraM. Karsai and A. Vespignani, Controlling contagion processes in activity driven networks, Physical review letters, 112 (2014), 118702.  doi: 10.1103/PhysRevLett.112.118702.  Google Scholar

[13]

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.  Google Scholar

[14]

N. Perra, B. Gonçalves, R. Pastor-Satorras and A. Vespignani, Activity Driven Modeling of Time Varying Networks, Scientific Reports, 2012. doi: 10.1038/srep00469.  Google Scholar

[15]

N. PerraA. BaronchelliD. MocanuB. Gonc'calvesR. 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.  Google Scholar

[16]

A. RizzoB. 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.  Google Scholar

[17]

A. RizzoM. 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.  Google Scholar

[18]

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. Google Scholar

[19]

N. M. ShahtoriC. ScoglioA. 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.  Google Scholar

[20]

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.  Google Scholar

[21]

F. ShuaibR. GunnalaE. O. MusaF. J. MahoneyO. OguntimehinP. M. NgukuS. B. NyantiN. KnightN. S. GwarzoO. IdigbeA. Nasidi and J. F. Vertefeuille, Ebola virus disease outbreak-Nigeria, July-September 2014, MMWR Morb Mortal Wkly Rep, 63 (2014), 867-872.   Google Scholar

[22]

M. Starnini and R. Pastor-Satorras, Temporal percolation in activity-driven networks, Physical Review E, 89 (2014), 032807.  doi: 10.1103/PhysRevE.89.032807.  Google Scholar

[23]

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.  Google Scholar

[24]

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.  Google Scholar

[25]

L. ZinoA. 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.  Google Scholar

[26]

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. Google Scholar

[27]

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. Google Scholar

show all references

References:
[1]

C. BrowneH. 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.  Google Scholar

[2]

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.  Google Scholar

[3]

O. DiekmannJ. 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.  Google Scholar

[4]

M. G. Dixon and I. J. Schafer, Ebola Viral Disease Outbreak - West Africa, 2014, MMWR Morb Mortal Wkly Rep, 63 (2014), 548-551.   Google Scholar

[5]

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.  Google Scholar

[6]

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.  Google Scholar

[7]

M. GreinerD. 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.  Google Scholar

[8]

J. M. HeffernanR. 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.  Google Scholar

[9]

M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals, Princeton University Press, Princeton, NJ, 2008.  Google Scholar

[10]

I. Z. KissD. 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.  Google Scholar

[11]

D. KlinkenbergC. Fraser and H. Heesterbeek, The effectiveness of contact tracing in emerging epidemics, PloS One, 1 (2006), e12.  doi: 10.1371/journal.pone.0000012.  Google Scholar

[12]

S. LiuN. PerraM. Karsai and A. Vespignani, Controlling contagion processes in activity driven networks, Physical review letters, 112 (2014), 118702.  doi: 10.1103/PhysRevLett.112.118702.  Google Scholar

[13]

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.  Google Scholar

[14]

N. Perra, B. Gonçalves, R. Pastor-Satorras and A. Vespignani, Activity Driven Modeling of Time Varying Networks, Scientific Reports, 2012. doi: 10.1038/srep00469.  Google Scholar

[15]

N. PerraA. BaronchelliD. MocanuB. Gonc'calvesR. 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.  Google Scholar

[16]

A. RizzoB. 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.  Google Scholar

[17]

A. RizzoM. 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.  Google Scholar

[18]

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. Google Scholar

[19]

N. M. ShahtoriC. ScoglioA. 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.  Google Scholar

[20]

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.  Google Scholar

[21]

F. ShuaibR. GunnalaE. O. MusaF. J. MahoneyO. OguntimehinP. M. NgukuS. B. NyantiN. KnightN. S. GwarzoO. IdigbeA. Nasidi and J. F. Vertefeuille, Ebola virus disease outbreak-Nigeria, July-September 2014, MMWR Morb Mortal Wkly Rep, 63 (2014), 867-872.   Google Scholar

[22]

M. Starnini and R. Pastor-Satorras, Temporal percolation in activity-driven networks, Physical Review E, 89 (2014), 032807.  doi: 10.1103/PhysRevE.89.032807.  Google Scholar

[23]

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.  Google Scholar

[24]

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.  Google Scholar

[25]

L. ZinoA. 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.  Google Scholar

[26]

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. Google Scholar

[27]

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. Google Scholar

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 ($\gamma$) $0.33$
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 ($\eta_H$) $0.005$
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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