# Evaluating the Effectiveness of COVID-19 Bluetooth-Based Smartphone Contact Tracing Applications

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## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Smartphone-Based Contact Tracing

#### 3.1. Contact Tracing Applications

#### 3.2. Characterizing Contact Tracing Effectiveness

## 4. Epidemic Model

- $S\to I$: Infected individuals who are not traced and consequently, not quarantined. In general, the transmission rate, that is the rate in which the infection is transmitted from one infected individual to one susceptible individual, is formed from the product of the number of contacts per time unit k, and the probability to transmit the disease b; hence, newly infected individuals are generated with a whole rate $kbI\frac{S}{N}$. Note that this rate is for all infected individuals. Since in this transition we are only considering the infected ones that are not traced, the previous rate is multiplied by $(1-{q}_{i})$, that is the fraction of non-traced contacts, so that the transition rate is $(1-{q}_{i})kbI\frac{S}{N}$. The other fraction of infected individuals is considered in transition $S\to {Q}_{T}$.
- $S\to {Q}_{T}$: Infected individuals who are being traced and go directly to the tracing state. When infected individuals are detected (that is, when they are in class ${Q}_{T}$) their previous contacts that are in the susceptible class are traced, and some of them are quarantined. Therefore, this transition considers only the traced contacts, that is the fraction ${q}_{s}$, so the rate is ${q}_{i}kbI\frac{S}{N}$. It refers to the individuals that may have been infected during the day.
- $S\to {Q}_{S}$: Non-infected individuals traced and quarantined. The transition rate is ${q}_{s}k(1-b)I\frac{S}{N}$, considering that $(1-b)$ is the probability of not transmitting the disease. In this transition rate, the fraction ${q}_{s}$ considers the effect of false positives, which can increase the number of people unnecessarily quarantined.
- $I\to {Q}_{T}$: Detection of infected individuals, triggering the tracing of their previous contacts using the application while being quarantined. In our model, infected individuals are detected, traced and quarantined with $\delta $ rate, staying in quarantine for an average time of $1/{\tau}_{Q}$ days. Prior to going to the final quarantine class ${Q}_{I}$, these individuals stay during a short time $1/{\tau}_{T}$ in class ${Q}_{T}$, for tracing their previous contacts. This time $1/{\tau}_{T}$ is the tracing time ($TT$) that models the necessary time to trace the contacts, allowing to compare the fast-tracing centralized approach versus the slower-tracing decentralized approach.
- ${Q}_{T}\to {Q}_{I}$: This transition supposes the end of the tracing. After the tracing time $1/{\tau}_{T}$ they move to the ${Q}_{I}$ class, to finish their quarantine.
- ${Q}_{I}\to R$: End of quarantine and infection. In this class, individuals continue their quarantine for the remaining quarantine time, which is obtained as $1/{\tau}_{T}^{r}$ = $1/{\tau}_{Q}-1/{\tau}_{T}$, and, finally, they are considered recovered and move to the R class afterward.
- $I\to R$: Non detected infected individuals recovered from the disease. This transition considers those infected individuals not detected, that is, asymptomatic ones which have not been tested. The rate is simply the recovery rate $\gamma $.
- ${Q}_{S}\to S$: End of quarantine for susceptible individuals. After being quarantined, individuals in the ${Q}_{S}$ class return to the susceptible class, after staying in quarantine for $1/{\tau}_{Q}$ days.

`ode45`, which is the one used in this paper). For solving this model, we consider an initial value of $R\left(0\right)$ and $I\left(0\right)$ (that is, the number of recovered and infected individuals at the beginning of an outbreak). Note, that in most of our experiments these values $R\left(0\right)$, $I\left(0\right)$ are 0, as we consider an initial outbreak with no people infected or immunized. Then, the initial number of susceptible individuals is obtained as $S\left(0\right)=N-R\left(0\right)-I\left(0\right)$, and the other classes are zero. Next, the model is numerically solved for a given time (for example, one year), or until there are no infected individuals. That is when the sum of classes $I,{Q}_{I},{Q}_{T}$ is smaller than one, which means that the infection is over. In this case, the duration of the epidemic is obtained as the time t when $I\left(t\right)+{Q}_{T}\left(i\right)+{Q}_{I}\left(t\right)<1$.

## 5. Evaluation

#### 5.1. Impact of Utilization

#### 5.2. Impact of Accuracy

#### 5.3. Centralized vs. Decentralized Solutions

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Li, R.; Rivers, C.; Tan, Q.; Murray, M.B.; Toner, E.; Lipsitch, M. The demand for inpatient and ICU beds for COVID-19 in the US: Lessons from Chinese cities. medRxiv
**2020**. [Google Scholar] [CrossRef] [Green Version] - COVID-19 National Emergency Response Center, Epidemiology and Case Management Team, Korea Centers for Disease Control and Prevention. Contact Transmission of COVID-19 in South Korea: Novel Investigation Techniques for Tracing Contacts. Osong Public Health Res Perspect
**2020**, 11, 60–63. [Google Scholar] [CrossRef] [Green Version] - Eames, K.; Keeling, M. Contact Tracing and Disease Control. Proc. Biol. Sci. R. Soc.
**2004**, 270, 2565–2571. [Google Scholar] [CrossRef] [Green Version] - Salathé, M. Digital epidemiology: What is it, and where is it going? Life Sci. Soc. Policy
**2018**, 14, 1. [Google Scholar] [CrossRef] - Computer Laboratory-University of Cambridge. The FluPhone Study. 2010. Available online: https://www.fluphone.org (accessed on 24 May 2020).
- Singapore Government. Tracetogether. 2020. Available online: https://www.tracetogether.gov.sg (accessed on 15 April 2020).
- MIT. Safe Paths. 2020. Available online: http://safepaths.mit.edu (accessed on 22 April 2020).
- Raskar, R.; Schunemann, I.; Barbar, R.; Vilcans, K.; Gray, J.; Vepakomma, P.; Kapa, S.; Nuzzo, A.; Gupta, R.; Berke, A.; et al. Apps Gone Rogue: Maintaining Personal Privacy in an Epidemic. arXiv
**2020**, arXiv:2003.08567. [Google Scholar] - PePP-PT e.V. i.Gr. Pan-European Privacy-Preserving Proximity Tracing (PEPP-PT). 2020. Available online: https://www.pepp-pt.org (accessed on 15 September 2020).
- Pelusi, L.; Passarella, A.; Conti, M. Opportunistic networking: Data forwarding in disconnected mobile ad hoc networks. Commun. Mag. IEEE
**2006**, 44, 134–141. [Google Scholar] [CrossRef] - Zhang, X.; Neglia, G.; Kurose, J.; Towsley, D. Performance modeling of epidemic routing. Comput. Netw.
**2007**, 51, 2867–2891. [Google Scholar] [CrossRef] - Helgason, Ó.; Kouyoumdjieva, S.T.; Karlsson, G. Opportunistic Communication and Human Mobility. IEEE Trans. Mob. Comput.
**2014**, 13, 1597–1610. [Google Scholar] [CrossRef] - Chancay-García, L.; Hernández-Orallo, E.; Manzoni, P.; Calafate, C.T.; Cano, J. Evaluating and Enhancing Information Dissemination in Urban Areas of Interest Using Opportunistic Networks. IEEE Access
**2018**, 6, 32514–32531. [Google Scholar] [CrossRef] - Dede, J.; Förster, A.; Hernández-Orallo, E.; Herrera-Tapia, J.; Kuladinithi, K.; Kuppusamy, V.; Manzoni, P.; bin Muslim, A.; Udugama, A.; Vatandas, Z. Simulating Opportunistic Networks: Survey and Future Directions. IEEE Commun. Surv. Tutor.
**2018**, 20, 1547–1573. [Google Scholar] [CrossRef] [Green Version] - Hernández-Orallo, E.; Murillo-Arcila, M.; Calafate, C.T.; Cano, J.C.; Conejero, J.A.; Manzoni, P. Analytical evaluation of the performance of contact-Based messaging applications. Comput. Netw.
**2016**, 111, 45–54. [Google Scholar] [CrossRef] [Green Version] - Hernandez-Orallo, E.; Serrat Olmos, M.; Cano, J.C.; Calafate, C.; Manzoni, P. CoCoWa: A Collaborative Contact-Based Watchdog for Detecting Selfish Nodes. IEEE Trans. Mob. Comput.
**2015**, 14, 1162–1175. [Google Scholar] [CrossRef] [Green Version] - Hernández-Orallo, E.; Manzoni, P.; Calafate, C.T.; Cano, J. Evaluating How Smartphone Contact Tracing Technology Can Reduce the Spread of Infectious Diseases: The Case of COVID-19. IEEE Access
**2020**, 8, 99083–99097. [Google Scholar] [CrossRef] - Christaki, E. New technologies in predicting, preventing and controlling emerging infectious diseases. Virulence
**2015**, 6, 558–565. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Cecilia, J.M.; Cano, J.C.; Hernández-Orallo, E.; Calafate, C.T. Mobile crowdsensing approaches to address the COVID-19 pandemic in Spain. IET Smart Cities
**2020**, 2, 58–63. [Google Scholar] [CrossRef] - Hernández-Orallo, E.; Borrego, C.; Manzoni, P.; Marquez-Barja, J.M.; Cano, J.C.; Calafate, C.T. Optimising data diffusion while reducing local resources consumption in Opportunistic Mobile Crowdsensing. Pervasive Mob. Comput.
**2020**, 67, 101201. [Google Scholar] [CrossRef] - Doran, D.; Severin, K.; Gokhale, S.; Dagnino, A. Social media enabled human sensing for smart cities. AI Commun.
**2016**, 29, 57–75. [Google Scholar] [CrossRef] [Green Version] - Salathé, M.; Kazandjieva, M.; Lee, J.W.; Levis, P.; Feldman, M.W.; Jones, J.H. A high-resolution human contact network for infectious disease transmission. Proc. Natl. Acad. Sci. USA
**2010**, 107, 22020–22025. [Google Scholar] [CrossRef] [Green Version] - Fraser, C.; Riley, S.; Anderson, R.; Ferguson, N. Factors that make an infectious disease outbreak controllable. Proc. Natl. Acad. Sci. USA
**2004**, 101, 6146–6151. [Google Scholar] [CrossRef] [Green Version] - Klinkenberg, D.; Fraser, C.; Heesterbeek, H. The Effectiveness of Contact Tracing in Emerging Epidemics. PLoS ONE
**2006**, 1, e12. [Google Scholar] [CrossRef] - Kwok, K.O.; Tang, A.; Wei, V.W.; Park, W.H.; Yeoh, E.K.; Riley, S. Epidemic Models of Contact Tracing: Systematic Review of Transmission Studies of Severe Acute Respiratory Syndrome and Middle East Respiratory Syndrome. Comput. Struct. Biotechnol. J.
**2019**, 17, 186–194. [Google Scholar] [CrossRef] [PubMed] - Müller, J.; Kretzschmar, M.; Dietz, K. Contact tracing in stochastic and deterministic epidemic models. Math. Biosci.
**2000**, 164, 39–64. [Google Scholar] [CrossRef] - Huerta, R.; Tsimring, L.S. Contact tracing and epidemics control in social networks. Phys. Rev. E Stat. Nonlin. Soft Matter Phys.
**2002**, 66, 056115. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Lipsitch, M.; Cohen, T.; Cooper, B.; Robins, J.M.; Ma, S.; James, L.; Gopalakrishna, G.; Chew, S.K.; Tan, C.C.; Samore, M.H.; et al. Transmission dynamics and control of severe acute respiratory syndrome. Science
**2003**, 300, 1966–1970. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hellewell, J.; Abbott, S.; Gimma, A.; Bosse, N.I.; Jarvis, C.I.; Russell, T.W.; Munday, J.D.; Kucharski, A.J.; Edmunds, W.J.; Sun, F.; et al. Feasibility of controlling COVID-19 outbreaks by isolation of cases and contacts. Lancet Glob. Health
**2020**, 8, e488–e496. [Google Scholar] [CrossRef] [Green Version] - Farrahi, K.; Emonet, R.; Cebrian, M. Epidemic contact tracing via communication traces. PLoS ONE
**2014**, 9, e95133. [Google Scholar] [CrossRef] [PubMed] - Yang, H.X.; Wang, W.X.; Lai, Y.C.; Wang, B.H. Traffic-driven epidemic spreading on networks of mobile agents. EPL (Europhys. Lett.)
**2012**, 98, 68003. [Google Scholar] [CrossRef] - Leith, D.J.; Farrell, S. Coronavirus Contact Tracing: Evaluating the Potential of Using Bluetooth Received Signal Strength For Proximity Detection; Technical Report; School of Computer Science and Statistics, Trinity College: Dublin, Ireland, 2020. [Google Scholar]
- Kindt, P.H.; Chakraborty, T.; Chakraborty, S. How Reliable is Smartphone-based Electronic Contact Tracing for COVID-19? arXiv
**2020**, arXiv:2005.05625. [Google Scholar] - Anglemyer, A.; Moore, T.; Parker, L.; Chambers, T.; Grady, A.; Chiu, K.; Parry, M.; Wilczynska, M.; Flemyng, E.; Bero, L. Digital contact tracing technologies in epidemics: A rapid review. Cochrane Database Syst. Rev.
**2020**. [Google Scholar] [CrossRef] - Braithwaite, I.; Callender, T.; Bullock, M.; Aldridge, R.W. Automated and partly automated contact tracing: A systematic review to inform the control of COVID-19. Lancet Digit. Health
**2020**, 9, 5. [Google Scholar] [CrossRef] - Ferretti, L.; Wymant, C.; Kendall, M.; Zhao, L.; Nurtay, A.; Abeler-Dorner, L.; Parker, M.; Bonsall, D.; Fraser, C. Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing. Science
**2020**, 368, 6491. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Cencetti, G.; Santin, G.; Longa, A.; Pigani, E.; Barrat, A.; Cattuto, C.; Lehmann, S.; Lepri, B. Using real-world contact networks to quantify the effectiveness of digital contact tracing and isolation strategies for Covid-19 pandemic. medRxiv
**2020**. [Google Scholar] [CrossRef] - Kretzschmar, M.E.; Rozhnova, G.; Bootsma, M.; van Boven, M.E.; van de Wijgert, J.; Bonten, M. Time is of the essence: Impact of delays on effectiveness of contact tracing for COVID-19. medRxiv
**2020**. [Google Scholar] [CrossRef] - Lambert, A. A mathematical assessment of the efficiency of quarantining and contact tracing in curbing the COVID-19 epidemic. medRxiv
**2020**. [Google Scholar] [CrossRef] - Sattler, F.; Ma, J.; Wagner, P.; Neumann, D.; Wenzel, M.; Schäfer, R.; Wiegand, T. Risk estimation of SARS-CoV-2 transmission from bluetooth low energy measurements. NPJ Digit. Med.
**2020**, 3, 1. [Google Scholar] [CrossRef] - Pueyo, T. Coronavirus: How to Do Testing and Contact Tracing. Medium. 2020. Available online: https://medium.com/@tomaspueyo (accessed on 11 June 2020).
- Li, R.; Pei, S.; Chen, B.; Song, Y.; Zhang, T.; Yang, W.; Shaman, J. Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2). Science
**2020**, 368, 489–493. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Centralized vs. decentralized contact tracing approaches: (

**a**) when two users’ smartphones are in range, they exchange their anonymous key codes; (

**b**) when an individual is detected as positive, he/she notifies the application of his/her this new status; in the centralized approach (

**c**), the smartphone uploads its key and also the other keys gathered from its previous contacts; (

**d**) the possible risk contacts are detected using the centralized servers; in the decentralized approach (

**e**), the smartphone only uploads its key; and (

**f**) all keys of detected positives are downloaded by the application and the matching is performed locally.

**Figure 2.**Epidemic dynamics with different mobile contact tracing utilization for COVID-19 infection. (

**a**) No measures ($\delta =q=0$); (

**b**) detection and isolation of individuals, no contact tracing ($\delta =0.05$, $U=0$); (

**c**) with mobile contact tracing (optimistic utilization) ($\delta =0.05$, $U=0.7,RC=0.8$); (

**d**) with mobile contact tracing (pessimistic utilization) ($\delta =0.05$, $U=0.5,RC=0.5$).

**Figure 3.**Contact tracing application utilization thresholds for controlling an infection, considering different values of reproduction ratio (${R}_{0}$) and percentage of susceptible people ($S/N$). The pair of values above the lines results in a disease-free equilibrium.

**Figure 4.**Efficiency of the contact tracing application depending on utilization: (

**a**,

**b**) percentage of population infected and quarantined for ${R}_{0}=3$; (

**c**,

**d**) percentage of population infected and quarantined considering other measures (for ${R}_{0}=2$); (

**d**) proportion of population quarantined considering also other measures ($R\left(0\right)=2$).

**Figure 5.**Impact of accuracy. That is, the impacts of false positive and false negative ratios on the efficiency of contact tracing. All plots are for ${R}_{0}=3$, $1/{\tau}_{T}=1$ day and $RC=0.6$: (

**a**) percentage of population infected; (

**b**) percentage of population quarantined.

**Figure 6.**Efficiency of the contact tracing application considering the tracing time (all plots are for ${R}_{0}=2$): (

**a**,

**b**) percentage of population infected and quarantined when tracing time is 2 days ($TT=2$); (

**c**,

**d**) percentage of population infected and quarantined considering when tracing time is 4 days ($TT=4$).

Symbol | Definition |
---|---|

N | Population |

$S,I,R$ | Susceptible, Infected and Recovered classes |

${Q}_{S}$ | Class of susceptible individuals in quarantine by contact tracing |

${Q}_{I}$ | Class of infected individuals detected and quarantined. |

${Q}_{T}$ | Class of infected individuals detected, quarantined and being traced. |

${Q}_{a}$ | People quarantined by contact tracing. |

${R}_{0}$ | Basic/effective reproductive number (${R}_{0}=kb/\gamma =\beta /\gamma $) |

k | Average contacts per individual and time unit (days). |

b | Probability to transmit the disease. |

$\delta $ | Detection rate of infected individuals |

$\beta $ | Transmission rate |

$\gamma $ | Recovery rate (that is, $1/\gamma $ = days to recover) |

$1/{\tau}_{Q}$ | Average duration of the quarantine |

$1/{\tau}_{Q}^{r}$ | Average duration of the remaining quarantine (that is, $1/{\tau}_{Q}-1/{\tau}_{T}$) |

$1/{\tau}_{T}$ | Average tracing time (also $TT$) |

$FN$ | False negative ratio |

$FP$ | False positive ratio |

U | Ratio of user using the application |

$RC$ | Ratio of users checking for exposure |

${q}_{i}$,${q}_{s}$ | Estimated fraction of traced contacts (normalized) |

Parameter | Estimated Value |
---|---|

${R}_{0}$ | 3 (1.5–6) |

$\gamma $ | 1/15 |

$\beta $ | 0.52 |

${\tau}_{Q}$ | 1/14 |

$\delta $ | 0.05 (0.02–0.1) |

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**MDPI and ACS Style**

Hernández-Orallo, E.; Calafate, C.T.; Cano, J.-C.; Manzoni, P.
Evaluating the Effectiveness of COVID-19 Bluetooth-Based Smartphone Contact Tracing Applications. *Appl. Sci.* **2020**, *10*, 7113.
https://doi.org/10.3390/app10207113

**AMA Style**

Hernández-Orallo E, Calafate CT, Cano J-C, Manzoni P.
Evaluating the Effectiveness of COVID-19 Bluetooth-Based Smartphone Contact Tracing Applications. *Applied Sciences*. 2020; 10(20):7113.
https://doi.org/10.3390/app10207113

**Chicago/Turabian Style**

Hernández-Orallo, Enrique, Carlos T. Calafate, Juan-Carlos Cano, and Pietro Manzoni.
2020. "Evaluating the Effectiveness of COVID-19 Bluetooth-Based Smartphone Contact Tracing Applications" *Applied Sciences* 10, no. 20: 7113.
https://doi.org/10.3390/app10207113