Mathematical model for SARS-CoV-2 transmission and wastewater dynamics on Emory University campus Open Access

Boutelle, Cassandra (Summer 2022)

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Since the start of the SARS-CoV-2 pandemic, wastewater-based epidemiology approaches for surveillance developed rapidly to fill gaps left by traditional clinical surveillance systems. This study aims to quantify how wastewater and infection dynamics changed in response to public health interventions and the emergence of variants. We use an SEIR-like model to simulate COVID-19 dynamics on Emory University campus over the 2020-2021 and 2021-2022 academic years. The model was run over five time periods with distinct viral dynamics and university policies: 1) No vaccination 1, no vaccines + no weekly screening. 2) No vaccination 2, no vaccines + weekly screening. 3) Vaccine rollout, active vaccination rate + weekly screening. 4) Delta, vaccination requirement + Delta variant predominance. 5) Omicron, booster vaccination requirement + Omicron variant predominance. Model parameters were defined using values from literature, except for the reproduction number and duration of infectious period which were calibrated for each time period. Infection dynamics of the model were validated by assessing the percent error between newly infectious individuals and new cases reported by Emory University. The average percent error was 2.9% for no vaccination 1, -3.4% for no vaccination 2, -13.2% for vaccine rollout, -11.8% for Delta, and -11.5% for Omicron. The wastewater dynamics of the model were validated for the first two time periods, when wastewater sampling occurred on campus. Simulated SARS-CoV-2 concentration in wastewater was consistent with swab positivity data for no vaccination 1 and 2. For the latter three periods, SARS-CoV-2 concentration was highest at the beginning of the period and then decreased over time. However, the model predicted that SARS-CoV-2 concentration would largely remain above the limit of detection throughout the time periods. Simulated SARS-CoV-2 concentrations briefly dropped below the limit of detection for the sampling method at the end of the Fall 2021 semester (Delta period). Quantitative assays for wastewater surveillance may be more useful when COVID-19 incidence is moderate or high. In the vaccine rollout and Omicron periods, a peak in predicted virus concentration in wastewater preceded a peak in reported cases by 5-17 days and could be used as an early warning for community incidence.

Table of Contents

Table of Contents

1   Introduction                                                                                                                     1

1.1   Background on 2019 SARS-CoV-2 Pandemic                                       1

1.2   Wastewater surveillance for SARS-CoV-2                                                               1

1.3   SARS-CoV-2 vaccine development and emergence of variants                        2

1.4   Objectives                                                                                                     4

2   Methods                                                                                                                            5

2.1   Mathematical model                                                                                               5

2.1.1   Model structure                                                                                                  6

2.1.2   Model parameterization and initialization                                                    8

2.2   Model validation                                                                                                     10

2.3   Model analysis                                                                                                         11

3   Results                                                                                                                              12

3.1   Model validation results                                                                                        12

3.1.1   Validation of transmission dynamics                                                            12

3.1.2   Validation of wastewater dynamics                                                               13

3.2   Model simulation and projection results                                                          14

4   Discussion                                                                                                                       15

4.1   Validation                                                                                                                15

4.2   Simulation and Prediction                                                                                   16

4.3   Limitations                                                                                                              18

5   Conclusion                                                                                                                      19

Figures, Tables, and Equations                                                                                         20

Figure 1                                                                                                                              21

Figure 2                                                                                                                              22

Equations 1-18                                                                                                                 23

Table 1                                                                                                                                24

Equations 19-20                                                                                                               26

Table 2                                                                                                                                26

Figure 3                                                                                                                               27

Figure 4                                                                                                                               28

Figure 5                                                                                                                               29

Figure 6                                                                                                                               30

Table 3                                                                                                                                 32

References                                                                                                                               33

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