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Phan T, Brozak S, Pell B, Oghuan J, Gitter A, Hu T, Ribeiro RM, Ke R, Mena KD, Perelson AS, Kuang Y, Wu F. Making waves: Integrating wastewater surveillance with dynamic modeling to track and predict viral outbreaks. Water Res 2023; 243:120372. [PMID: 37494742 DOI: 10.1016/j.watres.2023.120372] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2023] [Revised: 07/10/2023] [Accepted: 07/15/2023] [Indexed: 07/28/2023]
Abstract
Wastewater surveillance has proved to be a valuable tool to track the COVID-19 pandemic. However, most studies using wastewater surveillance data revolve around establishing correlations and lead time relative to reported case data. In this perspective, we advocate for the integration of wastewater surveillance data with dynamic within-host and between-host models to better understand, monitor, and predict viral disease outbreaks. Dynamic models overcome emblematic difficulties of using wastewater surveillance data such as establishing the temporal viral shedding profile. Complementarily, wastewater surveillance data bypasses the issues of time lag and underreporting in clinical case report data, thus enhancing the utility and applicability of dynamic models. The integration of wastewater surveillance data with dynamic models can enhance real-time tracking and prevalence estimation, forecast viral transmission and intervention effectiveness, and most importantly, provide a mechanistic understanding of infectious disease dynamics and the driving factors. Dynamic modeling of wastewater surveillance data will advance the development of a predictive and responsive monitoring system to improve pandemic preparedness and population health.
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Affiliation(s)
- Tin Phan
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, NM 87544, USA
| | - Samantha Brozak
- School of Mathematical and Statistical Sciences, Arizona State University, AZ 85281, USA
| | - Bruce Pell
- Department of Mathematics and Computer Science, Lawrence Technological University, MI 48075, USA
| | - Jeremiah Oghuan
- School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX 77030, USA
| | - Anna Gitter
- School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX 77030, USA
| | - Tao Hu
- Department of Geography, Oklahoma State University, Stillwater, OK 74078, USA
| | - Ruy M Ribeiro
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, NM 87544, USA
| | - Ruian Ke
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, NM 87544, USA
| | - Kristina D Mena
- School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX 77030, USA; Texas Epidemic Public Health Institute, Houston, TX 77030, USA
| | - Alan S Perelson
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, NM 87544, USA; Santa Fe Institute, Santa Fe, NM 87501, USA
| | - Yang Kuang
- School of Mathematical and Statistical Sciences, Arizona State University, AZ 85281, USA
| | - Fuqing Wu
- School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX 77030, USA; Texas Epidemic Public Health Institute, Houston, TX 77030, USA.
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Phan T, Brozak S, Pell B, Ciupe SM, Ke R, Ribeiro RM, Gitter A, Mena KD, Perelson AS, Kuang Y, Wu F. Prolonged viral shedding from noninfectious individuals confounds wastewater-based epidemiology. medRxiv 2023:2023.06.08.23291144. [PMID: 37333173 PMCID: PMC10274979 DOI: 10.1101/2023.06.08.23291144] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/20/2023]
Abstract
Wastewater surveillance has been widely used to track and estimate SARS-CoV-2 incidence. While both infectious and recovered individuals shed virus into wastewater, epidemiological inferences using wastewater often only consider the viral contribution from the former group. Yet, the persistent shedding in the latter group could confound wastewater-based epidemiological inference, especially during the late stage of an outbreak when the recovered population outnumbers the infectious population. To determine the impact of recovered individuals' viral shedding on the utility of wastewater surveillance, we develop a quantitative framework that incorporates population-level viral shedding dynamics, measured viral RNA in wastewater, and an epidemic dynamic model. We find that the viral shedding from the recovered population can become higher than the infectious population after the transmission peak, which leads to a decrease in the correlation between wastewater viral RNA and case report data. Furthermore, the inclusion of recovered individuals' viral shedding into the model predicts earlier transmission dynamics and slower decreasing trends in wastewater viral RNA. The prolonged viral shedding also induces a potential delay in the detection of new variants due to the time needed to generate enough new cases for a significant viral signal in an environment dominated by virus shed by the recovered population. This effect is most prominent toward the end of an outbreak and is greatly affected by both the recovered individuals' shedding rate and shedding duration. Our results suggest that the inclusion of viral shedding from non-infectious recovered individuals into wastewater surveillance research is important for precision epidemiology.
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Affiliation(s)
- Tin Phan
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, NM 87544, USA
| | - Samantha Brozak
- School of Mathematical and Statistical Sciences, Arizona State University, AZ 85281, USA
| | - Bruce Pell
- Department of Mathematics and Computer Science, Lawrence Technological University, MI 48075, USA
| | - Stanca M. Ciupe
- Department of Mathematics, Virginia Tech, Blacksburg, VA 24060, USA
| | - Ruian Ke
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, NM 87544, USA
| | - Ruy M. Ribeiro
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, NM 87544, USA
| | - Anna Gitter
- School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX 77030, USA
- Texas Epidemic Public Health Institute, TX, USA
| | - Kristina D. Mena
- School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX 77030, USA
- Texas Epidemic Public Health Institute, TX, USA
| | - Alan S. Perelson
- Theoretical Biology and Biophysics, Los Alamos National Laboratory, NM 87544, USA
- Santa Fe Institute, Santa Fe, NM 87501, USA
| | - Yang Kuang
- School of Mathematical and Statistical Sciences, Arizona State University, AZ 85281, USA
| | - Fuqing Wu
- School of Public Health, The University of Texas Health Science Center at Houston, Houston, TX 77030, USA
- Texas Epidemic Public Health Institute, TX, USA
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Pell B, Brozak S, Phan T, Wu F, Kuang Y. The emergence of a virus variant: dynamics of a competition model with cross-immunity time-delay validated by wastewater surveillance data for COVID-19. J Math Biol 2023; 86:63. [PMID: 36988621 PMCID: PMC10054223 DOI: 10.1007/s00285-023-01900-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2022] [Revised: 12/28/2022] [Accepted: 03/12/2023] [Indexed: 03/30/2023]
Abstract
We consider the dynamics of a virus spreading through a population that produces a mutant strain with the ability to infect individuals that were infected with the established strain. Temporary cross-immunity is included using a time delay, but is found to be a harmless delay. We provide some sufficient conditions that guarantee local and global asymptotic stability of the disease-free equilibrium and the two boundary equilibria when the two strains outcompete one another. It is shown that, due to the immune evasion of the emerging strain, the reproduction number of the emerging strain must be significantly lower than that of the established strain for the local stability of the established-strain-only boundary equilibrium. To analyze the unique coexistence equilibrium we apply a quasi steady-state argument to reduce the full model to a two-dimensional one that exhibits a global asymptotically stable established-strain-only equilibrium or global asymptotically stable coexistence equilibrium. Our results indicate that the basic reproduction numbers of both strains govern the overall dynamics, but in nontrivial ways due to the inclusion of cross-immunity. The model is applied to study the emergence of the SARS-CoV-2 Delta variant in the presence of the Alpha variant using wastewater surveillance data from the Deer Island Treatment Plant in Massachusetts, USA.
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Affiliation(s)
- Bruce Pell
- Mathematics and Computer Science Department, Lawrence Technological University, 21000 W. 10 Mile Rd, Southfield, MI, 48075, USA.
| | - Samantha Brozak
- School of Mathematical and Statistical Sciences, Arizona State University, 901 S. Palm Walk, Tempe, AZ, 85287-1804, USA
| | - Tin Phan
- Theoretical Biology and Biophysics Group, Houston, Los Alamos, NM, 87545, USA
| | - Fuqing Wu
- Texas Epidemic Public Health Institute, Houston, TX, 77030, USA
- Department of Epidemiology, Human Genetics and Environmental Sciences, School of Public Health, The University of Texas Health Science Center at Houston, Houston, Texas, 77030, USA
| | - Yang Kuang
- School of Mathematical and Statistical Sciences, Arizona State University, 901 S. Palm Walk, Tempe, AZ, 85287-1804, USA
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Phan T, Brozak S, Pell B, Gitter A, Xiao A, Mena KD, Kuang Y, Wu F. A simple SEIR-V model to estimate COVID-19 prevalence and predict SARS-CoV-2 transmission using wastewater-based surveillance data. Sci Total Environ 2023; 857:159326. [PMID: 36220466 PMCID: PMC9547654 DOI: 10.1016/j.scitotenv.2022.159326] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2022] [Revised: 09/15/2022] [Accepted: 10/05/2022] [Indexed: 06/12/2023]
Abstract
Wastewater-based surveillance (WBS) has been widely used as a public health tool to monitor SARS-CoV-2 transmission. However, epidemiological inference from WBS data remains understudied and limits its application. In this study, we have established a quantitative framework to estimate COVID-19 prevalence and predict SARS-CoV-2 transmission through integrating WBS data into an SEIR-V model. We conceptually divide the individual-level viral shedding course into exposed, infectious, and recovery phases as an analogy to the compartments in a population-level SEIR model. We demonstrated that the effect of temperature on viral losses in the sewer can be straightforwardly incorporated in our framework. Using WBS data from the second wave of the pandemic (Oct 02, 2020-Jan 25, 2021) in the Greater Boston area, we showed that the SEIR-V model successfully recapitulates the temporal dynamics of viral load in wastewater and predicts the true number of cases peaked earlier and higher than the number of reported cases by 6-16 days and 8.3-10.2 folds (R = 0.93). This work showcases a simple yet effective method to bridge WBS and quantitative epidemiological modeling to estimate the prevalence and transmission of SARS-CoV-2 in the sewershed, which could facilitate the application of wastewater surveillance of infectious diseases for epidemiological inference and inform public health actions.
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Affiliation(s)
- Tin Phan
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, NM, USA
| | - Samantha Brozak
- School of Mathematical and Statistical Sciences, Arizona State University, AZ, USA
| | - Bruce Pell
- Department of Mathematics and Computer Science, Lawrence Technological University, MI, USA
| | - Anna Gitter
- The University of Texas Health Science Center at Houston, School of Public Health, Houston, TX, USA 77030
| | - Amy Xiao
- Center for Microbiome Informatics and Therapeutics; Department of Biological Engineering, Massachusetts Institute of Technology
| | - Kristina D Mena
- The University of Texas Health Science Center at Houston, School of Public Health, Houston, TX, USA 77030
| | - Yang Kuang
- School of Mathematical and Statistical Sciences, Arizona State University, AZ, USA.
| | - Fuqing Wu
- The University of Texas Health Science Center at Houston, School of Public Health, Houston, TX, USA 77030.
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Phan T, Brozak S, Pell B, Gitter A, Mena KD, Kuang Y, Wu F. A simple SEIR-V model to estimate COVID-19 prevalence and predict SARS-CoV-2 transmission using wastewater-based surveillance data. medRxiv 2022:2022.07.17.22277721. [PMID: 35898336 PMCID: PMC9327624 DOI: 10.1101/2022.07.17.22277721] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
Wastewater-based surveillance (WBS) has been widely used as a public health tool to monitor SARS-CoV-2 transmission. However, epidemiological inference from WBS data remains understudied and limits its application. In this study, we have established a quantitative framework to estimate COVID-19 prevalence and predict SARS-CoV-2 transmission through integrating WBS data into an SEIR-V model. We conceptually divide the individual-level viral shedding course into exposed, infectious, and recovery phases as an analogy to the compartments in population-level SEIR model. We demonstrated that the temperature effect on viral losses in the sewer can be straightforwardly incorporated in our framework. Using WBS data from the second wave of the pandemic (Oct 02, 2020 â€" Jan 25, 2021) in the Great Boston area, we showed that the SEIR-V model successfully recapitulates the temporal dynamics of viral load in wastewater and predicts the true number of cases peaked earlier and higher than the number of reported cases by 16 days and 8.6 folds ( R = 0.93), respectively. This work showcases a simple, yet effective method to bridge WBS and quantitative epidemiological modeling to estimate the prevalence and transmission of SARS-CoV-2 in the sewershed, which could facilitate the application of wastewater surveillance of infectious diseases for epidemiological inference and inform public health actions.
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Affiliation(s)
- Tin Phan
- Theoretical Biology and Biophysics Group, Los Alamos National Laboratory, New Mexico, USA
| | - Samantha Brozak
- School of Mathematical and Statistical Sciences, Arizona State University, Arizona, USA
| | - Bruce Pell
- Department of Mathematics and Computer Science, Lawrence Technological University, MI, USA
| | - Anna Gitter
- The University of Texas Health Science Center at Houston, School of Public Health, Houston, Texas, USA 77030
| | - Kristina D. Mena
- The University of Texas Health Science Center at Houston, School of Public Health, Houston, Texas, USA 77030
| | - Yang Kuang
- School of Mathematical and Statistical Sciences, Arizona State University, Arizona, USA
| | - Fuqing Wu
- The University of Texas Health Science Center at Houston, School of Public Health, Houston, Texas, USA 77030
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