Potentially informative. The main claims made are not strongly justified by the methods and data, but may yield some insight. The results and conclusions of the study may resemble those from the hypothetical ideal study, but there is substantial room for doubt. Decision-makers should consider this evidence only with a thorough understanding of its weaknesses, alongside other evidence and theory. Decision-makers should not consider this actionable, unless the weaknesses are clearly understood and there is other theory and evidence to further support it.
The basic ideas and importance of contact tracing in COVID-19 disease transmission are well justified by the authors. The article nicely described contact tracing methods during COVID-19 and their impact in the U.S. and some other countries. The authors, using Markov chain modelling, estimated the efficiency of identifying virus transmission through contact tracing. The method of collecting parameter values through a literature search and tabulating them for the readers is nice.
Overall conclusions on the U.S. contact tracing results can be validated through the online codes made available by the authors, but their accuracy in determining the population level disease spread and contact pairing is difficult to validate in the U.S. population.
Additional observations on the article and on contact tracing methods, and models are as follows:
It needs to be cautioned that any results and inferences on transmission probabilities obtained from contact tracing models and methods need to confine to the geographical region from which the data is collected. Too much extrapolating of parameter values obtained from a region to other regions or other non-homogeneous populations could be taken as an academic exercise. Such extrapolated results' conclusions on disease spread are difficult to ascertain for their uncertainty.
A contact tracing model built on one kind of data in a location to understand an infectious disease spread need not predict disease transmission in another location accurately.
In general, a complete contact tracing of the infected and reporting of the same is not possible due to several unavoidable reasons, for example, an infected who never went for any COVID-19 testing, etc. . The contact tracing methods cannot estimate 100% of all the transmissions that occurred retrospectively and not recorded. The range of cases identifiable through contact tracing depends on the data that was collected despite having any powerful methods. There are ethical issues that need to be strictly adhered to in following an index-positive individual and if any transmission of virus among the contacts. Epidemic control should be the primary objective than the aim of observing the disease transmission through contact tracing.
Let 𝑌𝑡 be the number of positive individuals tested at time 𝑡. Suppose 𝐶1, 𝐶2, … , 𝐶𝑌𝑡 be the number of contacts of 𝑌𝑡 individuals. Suppose 𝜌(𝐶𝑗) for 𝑗 = 1,2, … 𝑌𝑡 be the proportion of individuals who tested positive among 𝐶𝑗 during (𝑡, Δ𝑡]. The pairs of contacts for each of 𝑌𝑡 are expressed in the matrix 𝑀 of dimension (𝐶1 × 𝑌𝑡 ), where
The probability of transmission of the virus, say β, between all the pairs of contacts of Yt during (t, Δt] is
Note that if C1 = C2 = ⋯ = CYt = 1, then the number of pairs formed is exactly Yt. Then the probability of transmission during (t, Δt] is
where ρ(Yt) is the number of onward positive cases among Yt pairs during (t, Δt]. If every pair has resulted in a transmission, then probability of transmission is one. If one or more Cj values are > 1 and the pairs resulted in a transmission are traced then β can be computed with a certainty.
The steps indicated in M and β can be extended beyond the interval (t, Δt] to obtain disease spread beyond Δt. Let pSI (t,Δt] be the probability of transition of an individual who was susceptible (S) at time t got infected (I) during (t, Δt] and let X be a random variable describing the status of infectivity of an individual, then
A detailed contact tracing data also helpful in accurate estimation of the basic reproductive rate for an epidemic . Parameters in a continuous time Markov models can be obtained in several simulation studies, for example, see [3-5]. Mobile phone-based apps could be of great use in contact tracing [6, 7].
In conclusion, contact tracing based on a small sample of data in the U.S. could have been possible during the pandemic years 2020-2023 through retrospective and detailed pair formation methods explained.
1. Krantz, S., & Rao, A. (2020). Level of underreporting including underdiagnosis before the first peak of COVID-19 in various countries: Preliminary retrospective results based on wavelets and deterministic modeling. Infection Control &Hospital Epidemiology, 41(7), 857-859. doi:10.1017/ice.2020.116
2. Srinivasa Rao, A., Krantz, S., Bonsall, M., Kurien, T., Byrareddy, S., Swanson, D., Ramesh Bhat, and Sudhakar, K. (2022). How relevant is the basic reproductive number computed during the coronavirus disease 2019 (COVID-19) pandemic, especially during lockdowns? Infection Control & Hospital Epidemiology, 43(1), 125-127. doi:10.1017/ice.2020.1376
3. Al-Zoughool, Mustafa, et al. "Using a stochastic continuous-time Markov chain model to examine alternative timing and duration of the COVID-19 lockdown in Kuwait: what can be done now?." Archives of Public Health 80.1 (2022): 22.
4. Lee, T.J., et al (2023). Markov Chain Models for Cardiac Rhythm Dynamics in Patients Undergoing Catheter Ablation of Atrial Fibrillation. Bull Math Biol 85, 34 (2023). https://doi.org/10.1007/s11538-023-01125-8
5. Stephano, M.A., Irunde, J.I., Mwasunda, J.A. et al. A continuous time Markov chain model for the dynamics of bovine tuberculosis in humans and cattle. Ricerche mat (2022). https://doi.org/10.1007/s11587-022-00696-3
6. Srinivasa Rao, A., & Vazquez, J. (2020). Identification of COVID-19 can be quicker through artificial intelligence framework using a mobile phone–based survey when cities and towns are under quarantine. Infection Control & Hospital Epidemiology, 41(7), 826-830. doi:10.1017/ice.2020.61
7. Coronavirus App to Provide At-Home Risk Assessment -- Campus Technology (accessed on May 2, 2023).
RR\ID acknowledges this review as an editorial on the preprint.