Modeling within-host and aerosol dynamics of SARS-CoV-2: The relationship with infectiousness

Abstract

The relationship between transmission of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and the amount of virus present in the proximity of a susceptible host is not understood. Here, we developed a within-host and aerosol mathematical model and used it to determine the relationship between viral kinetics in the upper respiratory track, viral kinetics in the aerosols, and new transmissions in golden hamsters challenged with SARS-CoV-2. We determined that infectious virus shedding early in infection correlates with transmission events, shedding of infectious virus diminishes late in the infection, and high viral RNA levels late in the infection are a poor indicator of transmission. We further showed that viral infectiousness increases in a density dependent manner with viral RNA and that their relative ratio is time-dependent. Such information is useful for designing interventions.

Fig 1. Model diagram.

Diagram for model Eqs (3) and (4).

Fig 2. % Weight change from baseline over time.

Weight functions (black lines) versus weight data (diamonds) in (A) males and females, (B) donors, and (C) contacts.

Fig 3. Infectious virus and viral RNA dynamics in upper respiratory tract and exhaled breath of male and female groups.

(Left panels) Dynamics of infectious virus V_u (red lines) and viral RNA R_u (blue lines) as given by model Eq 3 versus infectious viral titers (red circles) and RNA (blue diamonds) in the upper respiratory tract of the (A.) males and (B.) females; (Right panels) Dynamics of infectious virus V_a (red lines) and RNA molecules R_a (blue lines) as given by model Eq 4 versus infectious viral titers (red circles) and RNA (blue diamonds) in the exhaled breath of (A.) males and (B.) females. Model parameters are given in Table 1.

Fig 4. Infectious virus and viral RNA dynamics in upper respiratory tract of donor and contact groups.

Dynamics of infectious virus V_u (red lines) and viral RNA R_u (blue lines) as given by model Eq 3 versus infectious viral titers (red circles) and viral RNA (blue diamonds) in the upper respiratory tract of (A.) donors, (B.) contacts with fixed initial virus, V₀ = 1. Model parameters are given in Table 2.

Fig 5. Infectious virus as a function of total RNA.

Log10 infectious virus ν(R_u) as a function of total RNA R_u given by Eq (6) versus data (circles) in (A.) donors, (B.) contacts, (C.) males URT, and (D.) males aerosols. Parameters are given in Table 3.

Fig 6. Population dynamics of model variables.

Population dynamics of T, E, I, V_u, R_u, V_a and R_a as given by models Eqs 3 and 4 in (A.) males (back) and females (red) and (B.) donors (black), contacts with fixed inoculum V₀ = 1 TCID₅₀ (red). Model parameters are given in Tables 1 and 2.

Fig 7. Ratio of total RNA to infectious virus over time.

R_u/V_u over time versus data in representative donors (blue), contacts (red), males URT (gold), and males aerosols (pink) hamsters. The light data points correspond to data where the infectious virus is at the limit of detection.