A non-Markovian model to assess contact tracing for the containment of COVID-19

Authors: VAJDI, ARAM - Kansas State University; Cohnstaedt, Lee; Noronha, Leela; Mitzel, Dana; Wilson, William; SCOGLIO, CATERINA - Kansas State University

Submitted to: IEEE Access
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 6/10/2023
Publication Date: 7/10/2023
Citation: Vajdi, A., Cohnstaedt, L.W., Noronha, L.E., Mitzel, D.N., Wilson, W.C., Scoglio, C.M. 2023. A non-Markovian model to assess contact tracing for the containment of COVID-19. IEEE Access. 11(1): 197-211. https://doi.org/https://doi.org/10.1109/TNSE.2023.3293690.
DOI: https://doi.org/10.1109/TNSE.2023.3293690

Interpretive Summary: COVID-19 remains a challenging global threat with ongoing waves of infections and clinical disease which have resulted millions of deaths and an enormous strain on health systems worldwide. This paper evaluated the value of non-pharmaceutical interventions, such as social distancing, wearing face coverings, and contact tracing, which remain important tools, especially at the onset of an outbreak. To accomplish this, a new network-based mathematical model was developed using a non-Markovian (a non-exponential) distribution. This is an important accomplishment because most previous disease models use an exponential distribution of cases, which describes very few long duration cases and many short duration cases in a smooth curve. However, this distribution of cases does not always fit the available case data as was the situation with COVID-19. Therefore the conclusions of the models are biased by the incorrect distributions, this new model can account for any case distribution or duration resulting in more accurate predictions based on all the case data. The new model can also predict the shape of the epidemic, this is the rate of new cases, when the outbreak will peak, and how it will decline. Survey data during the 2020 fall academic semester from Kansas State University students and staff was used to validate the model. Model results determined that as few as four or five contacts was sufficient to maintain viral transmission. Additionally, the model reveals that contact tracing can be an effective outbreak mitigation measure by reducing the epidemic size by more than three-fold. Increasing the reliability of epidemic models is critical for accurate public health planning and use as decision support tools. For this reason, moving toward more accurate non-Markovian models built upon empirical data, such as the one proposed in this paper, is an important step in that direction.

Technical Abstract: COVID-19 remains a challenging global threat with ongoing waves of infections and clinical disease which have resulted millions of deaths and an enormous strain on health systems worldwide. Effective vaccines have been developed for the first variants of SARS-CoV-2 and administered to billions of people; however, the virus continues to circulate and evolve into new variants for which vaccines may ultimately be less effective. For this reason, non-pharmaceutical interventions, such as social distancing, wearing face coverings, and contact tracing, remain important tools, especially at the onset of an outbreak. In this paper, we assess the effectiveness of contact tracing using a non-Markovian, network-based mathematical model. To improve the reliability of the novel model, we incorporate empirically determined distributions for the transition time of model state pairs, such as from exposed to infected states. From a first-order closure approximation, we derive an expression for the epidemic threshold, which is dependent on the number of close contacts. Using survey data from a university population during the 2020 fall academic semester, we determined that even four to five contacts are sufficient to maintain viral transmission. Additionally, our model reveals that contact tracing can be an effective outbreak mitigation measure by reducing the epidemic size by more than three-fold. Increasing the reliability of epidemic models is critical for accurate public health planning and use as decision support tools. For this reason, moving toward more accurate non-Markovian models built upon empirical data, such as the one proposed in this paper, is an important step in that direction.