Probability of transmission of SARS-CoV-2 virus pathogens in long-distance passenger transport




SARS-CoV-2 pandemic, pathogen transmission, passenger transport


This paper presents a description of the methodology developed for estimation of pathogen transmission in transport and the results of the case study application for long-distance passenger transport. The primary objective is to report the method developed and the application for case studies in various passenger transport services. The most important findings and achievements of the presented study are the original universal methodology to estimate the probability of pathogen transmission with full mathematical disclosure and an open process formula, to make it possible to take other specific mechanisms of virus transmission when providing transport services. The results presented conducted an analysis on the mechanisms of transmission of SARS-CoV-2 virus pathogens during the transport process, to examine the chain of events as a result of which passengers may be infected. The author proposed a new method to estimate the probability of transmission of viral pathogens using the probability theory of the sum of elementary events. This is a new approach in this area, the advantage of which is a fully explicit mathematical formula that allows the method to be applied to various cases. The findings of this study can facilitate the management of epidemic risk in passenger transport operators and government administration. It should be clearly emphasised that the developed method and estimated values are the probabilities of pathogen transmission. Estimating the probability of transmission of the SARS-CoV-2 virus pathogen is not the same as the probability of viral infection, and more so the probability of contracting COVID-19. Viral infection strongly depends on viral mechanisms, exposure doses, and contact frequency. The probability of contracting COVID-19 and its complications depends on the individual characteristics of the immune system, even with confirmed viral infection. However, it is undoubtedly that the probability of transmission of the SARS-CoV-2 virus pathogen is the most reliable measure of infection risk, which can be estimated according to the objective determinants of pathogen transmission.


Aboubakr, H. A., Sharafeldin, T. A., & Goyal, S. M. (2020). Stability of SARS‐COV‐2 and other coronaviruses in the environment and on common touch surfaces and the influence of climatic conditions: A Review. Transboundary and Emerging Diseases, 68(2), 296–312.

Arias Velásquez, R.M., Mejía Lara, J.V., 2020a. Gaussian approach for probability and correlation between the number of COVID-19 cases and the air pollution in Lima. Urban Clim, 33.

Arias Velásquez, R.M., Mejía Lara, J.V., 2020b. Forecast and evaluation of COVID-19 spreading in USA with reduced-space Gaussian process regression. Chaos Solitons Fractals, 136.

Benmalek, E., Elmhamdi, J., Jilbab, A., & Jbari, A. (2023). A cough-based covid-19 detection with Gammatone and Mel-frequency cepstral coefficients. Diagnostyka, 24(2), 1–16.

Boone, S.A., Gerba, C.P., 2007. Significance of fomites in the spread of respiratory and enteric viral disease. Appl Environ Microbiol, 73, 1687–1696.

Bracher, J., Wolffram, D., Deuschel, J., Görgen, K., Ketterer, J.L., Ullrich, A., Abbott, S., Barbarossa, M. v., Bertsimas, D., Bhatia, S., Bodych, M., Bosse, N.I., Burgard, J.P., Castro, L., Fairchild, G., Fuhrmann, J., Funk, S., Gogolewski, K., Gu, Q., Heyder, S., Hotz, T., Kheifetz, Y., Kirsten, H., Krueger, T., Krymova, E., Li, M.L., Meinke, J.H., Michaud, I.J., Niedzielewski, K., Ożański, T., Rakowski, F., Scholz, M., Soni, S., Srivastava, A., Zieliński, J., Zou, D., Gneiting, T., Schienle, M., 2021. A pre-registered short-term forecasting study of COVID-19 in Germany and Poland during the second wave. Nature Communications, 12:1, 1–16.

Burdzik, R. (2022). Epidemic risk analysis and assessment in transport services: Covid-19 and other viruses. Boca Raton, USA: CRC Press, Taylor & Francis Group. ISBN 978-1-032-06961-6.

Burdzik, R. (2023). An application of the DHI methodology for a comparison of SARS-COV-2 epidemic hazards in Customer Delivery Services of Smart Cities. Smart Cities, 6(2), 965–986.

Burdzik, R., Chema, W., Celiński, I. (2023). A study on passenger flow model and simulation in aspect of COVID-19 spreading on public transport bus stops. Journal of Public Transportation, 25, 100063.

Burdzik, R., Speybroeck, N. (2023). Study on the estimation of SARS-CoV-2 virus pathogens’ transmission probabilities for different public bus transport service scenarios. Transport Problems, 18(3), 199-211.

CDC. Coronavirus Disease 2019 (COVID-19). 2020. Available at: Accessed 14 September 2021.

Chen, Y., Wang, Y., Wang, H., Hu, Z., Hua, L., 2020. Controlling urban traffic-one of the useful methods to ensure safety in Wuhan based on COVID-19 outbreak. Saf Sci, 131, 104938.

Colubri, A., Yadav, K., Jha, A., Sabeti, P.C., 2020. Individual-level Modeling of COVID-19 Epidemic Risk. arXiv:2006.16761v4.

Cori, L., Bianchi, F., Cadum, E., & Anthonj, C. (2020). Risk perception and covid-19. International Journal of Environmental Research and Public Health, 17(9), 3114.

Corzo, S. F., Godino, D. M., & Ramajo, D. E. (2022). Air circulation study inside and outside of urban buses induced by the opening of windows. Environmental Science and Pollution Research, 30(8), 20821–20832.

Dai, H., & Zhao, B. (2020). Association of infected probability of COVID-19 with ventilation rates in confined spaces: a Wells-Riley equation based investigation. medRxiv 2020.04. 21.20072397.

Dávid, A., Galieriková, A., Mako, P. (2022). Application of anti-epidemiological measures and covid-automat in public water transport. Transport Problems, 17(2), 189-197.

Esmailpour, J., Aghabayk, K., Aghajanzadeh, M., de Gruyter, C., 2022. Has COVID-19 changed our loyalty towards public transport? Understanding the moderating role of the pandemic in the relationship between service quality, customer satisfaction and loyalty. Transp Res Part A Policy Pract, 162, 80–103.

Flaxman, S., Mishra, S., Gandy, A., Unwin, H. J., Mellan, T. A., Coupland, H., Whittaker, C., Zhu, H., Berah, T., Eaton, J. W., Monod, M., Perez-Guzman, P. N., Schmit, N., Cilloni, L., Ainslie, K. E., Baguelin, M., Boonyasiri, A., Boyd, O., Cattarino, L., … Bhatt, S. (2020). Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe. Nature, 584(7820), 257–261.

Gogolewski, K., Miasojedow, B., Sadkowska-Todys, M., Stepień, M., Demkow, U., Lech, A., Szczurek, E., Rabczenko, D., Rosińska, M., Gambin, A., 2022. Data-driven case fatality rate estimation for the primary lineage of SARS-CoV-2 in Poland. Methods, 203, 584–593.

Graba, M., Bieniek, A., Prażnowski, K., Hennek, K., Mamala, J., Burdzik, R., Śmieja, M., 2023. Analysis of energy efficiency and dynamics during car acceleration. Eksploatacja i Niezawodność – Maintenance and Reliability, 25(1), 17.

He, X., Lau, E.H.Y., Wu, P., Deng, X., Wang, J., Hao, X., Lau, Y.C., Wong, J.Y., Guan, Y., Tan, X., Mo, X., Chen, Y., Liao, B., Chen, W., Hu, F., Zhang, Q., Zhong, M., Wu, Y., Zhao, L., Zhang, F., Cowling, B.J., Li, F., Leung, G.M., 2020. Temporal dynamics in viral shedding and transmissibility of COVID-19. Nat Med, 26, 672–675.

Hu, M., Lin, H., Wang, J., Xu, C., Tatem, A. J., Meng, B., Zhang, X., Liu, Y., Wang, P., Wu, G., Xie, H., & Lai, S. (2020). Risk of coronavirus disease 2019 transmission in train passengers: An epidemiological and modeling study. Clinical Infectious Diseases, 72(4), 604–610.

Karako, K., Song, P., Chen, Y., Tang, W., 2020. Analysis of COVID-19 infection spread in Japan based on stochastic transition model. Biosci Trends, 14, 134–138.

Katona, P., Kullar, R., & Zhang, K. (2022). Bringing transmission of severe acute respiratory syndrome coronavirus 2 (SARS-COV-2) to the surface: Is there a role for fomites? Clinical Infectious Diseases, 75(5), 910–916.

Kukulski, J., Lewczuk, K., Góra, I., & Wasiak, M. (2023). Methodological aspects of risk mapping in Multimode Transport Systems. Eksploatacja i Niezawodność – Maintenance and Reliability, 25(1), 19.

Kurek, A., & Macioszek, E. (2022). Daily variability of the use of parking spaces in the paid parking zone covered by dynamic parking information before and during the COVID-19 pandemic. Scientific Journal of Silesian University of Technology. Series Transport, 114, 55–65.

Lavezzo, E., Franchin, E., Ciavarella, C., Cuomo-Dannenburg, G., Barzon, L., Del Vecchio, C., Rossi, L., Manganelli, R., Loregian, A., Navarin, N., Abate, D., Sciro, M., Merigliano, S., De Canale, E., Vanuzzo, M. C., Besutti, V., Saluzzo, F., Onelia, F., Pacenti, M., … Ferguson, N. M. (2020). Suppression of a SARS-COV-2 outbreak in the Italian municipality of vo’. Nature, 584(7821), 425–429.

Mashrur, S.M., Wang, K., Habib, K.N., 2022. Will COVID-19 be the end for the public transit? Investigating the impacts of public health crisis on transit mode choice. Transp Res Part A Policy Pract, 164, 352–378.

Melikov, A. K., Ai, Z. T., & Markov, D. G. (2020). Intermittent occupancy combined with ventilation: An efficient strategy for the reduction of airborne transmission indoors. Science of The Total Environment, 744, 140908.

Murawski, J., Szczepański, E., Jacyna-Gołda, I., Izdebski, M., Jankowska-Karpa, D. (2022). Intelligent mobility: A model for assessing the safety of children traveling to school on a school bus with the use of intelligent bus stops. Eksploatacja i Niezawodność – Maintenance and Reliability, 24(4), 695-706.

Niewczas, A., Mórawski, Ł., Rymarz, J., Dębicka, E., & Hołyszko, P. (2023). Operational risk assessment model for city buses. Eksploatacja i Niezawodność – Maintenance and Reliability, 25(1), 14.

Park, J., & Kim, G. (2021). Risk of COVID-19 infection in public transportation: The development of a model. International Journal of Environmental Research and Public Health, 18(23), 12790.

Pitol, A. K., & Julian, T. R. (2021). Community transmission of SARS-COV-2 by surfaces: Risks and risk reduction strategies. Environmental Science & Technology Letters, 8(3), 263–269.

Ramajo, D. E., & Corzo, S. (2022). Airborne transmission risk in urban buses: A Computational Fluid Dynamics Study. Aerosol and Air Quality Research, 22(8), 210334.

Riley, E.C., Murphy, G., Riley, R.L. (1978). Airborne spread of measles in a suburban elementary school. American Journal of Epidemiology, 107(5), 421–432.

Rodriguez-Nava, G., Diekema, D. J., & Salinas, J. L. (2023). Reconsidering the routine use of contact precautions in preventing the transmission of severe acute respiratory coronavirus virus 2 (SARS-COV-2) in healthcare settings. Infection Control & Hospital Epidemiology, 44(6), 1035–1037.

Sangiorgio, V., & Parisi, F. (2020). A multicriteria approach for risk assessment of covid-19 in urban district lockdown. Safety Science, 130, 104862.

Science brief: SARS-CoV-2 and surface (fomite) transmission for indoor community environments. Centers for Disease Control and Prevention website. Published 2021. Accessed March 3, 2023.

Shafaghi, A. H., Rokhsar Talabazar, F., Koşar, A., & Ghorbani, M. (2020). On the effect of the respiratory droplet generation condition on COVID-19 transmission. Fluids, 5(3), 113.

Staniuk, W., Staniuk, M., Chamier-Gliszczynski, N., Jacyna, M., & Kłodawski, M. (2022). Decision-making under the risk, uncertainty and covid-19 pandemic conditions applying the PL9A method of logistics planning—case study. Energies, 15(2), 639.

Sun, C., & Zhai, Z. (2020). The efficacy of social distance and ventilation effectiveness in preventing COVID-19 transmission. Sustainable Cities and Society, 62, 102390.

Szaciłło, L., Jacyna, M., Szczepański, E., Izdebski, M. (2021). Risk assessment for rail freight transport operations. Eksploatacja i Niezawodność – Maintenance and Reliability, 23(3), 476-488.

Ulbrich, D., Selech, J., Kowalczyk, J., Jóźwiak, J., Durczak, K., Gil, L., Pieniak, D., Paczkowska, M., Przystupa, K. (2021). Reliability Analysis for Unrepairable Automotive Components. Materials, 14, 7014.

Verity, R., Okell, L. C., Dorigatti, I., Winskill, P., Whittaker, C., Imai, N., ... & Ferguson, N. M. (2020). Estimates of the severity of COVID-19 disease. MedRxiv, 2020-03.

Walker, P. G., Whittaker, C., Watson, O. J., Baguelin, M., Winskill, P., Hamlet, A., Djafaara, B. A., Cucunubá, Z., Olivera Mesa, D., Green, W., Thompson, H., Nayagam, S., Ainslie, K. E., Bhatia, S., Bhatt, S., Boonyasiri, A., Boyd, O., Brazeau, N. F., Cattarino, L., … Ghani, A. C. (2020). The impact of covid-19 and strategies for mitigation and suppression in low- and middle-income countries. Science, 369(6502), 413–422.

Xie, X., Li, Y., Chwang, A. T., Ho, P. L., & Seto, W. H. (2007). How far droplets can move in indoor environments - revisiting the wells evaporation - falling curve. Indoor Air, 17(3), 211–225.

Zafri, N. M., Khan, A., Jamal, S., & Alam, B. M. (2022a). Risk perceptions of COVID-19 transmission in different travel modes. Transportation Research Interdisciplinary Perspectives, 13, 100548.

Zhang, N., & Li, Y. (2018). Transmission of influenza A in a student office based on realistic person-to-person contact and surface touch behaviour. International Journal of Environmental Research and Public Health, 15(8), 1699.






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How to Cite

Burdzik, R. (2023). Probability of transmission of SARS-CoV-2 virus pathogens in long-distance passenger transport. Archives of Transport, 68(4), 21-39.


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