Individual-based model describing the transmission and spread of SARS-CoV-2 in the Belgian population

A recent study posted to the medRxiv* preprint server simulated the superspreading dynamics of coronavirus disease 2019 (COVID-19).

Background

Mathematical modeling studies have been instrumental in unraveling the dynamics of severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) transmission. Several studies have developed models accounting for many factors, including age, seasonality, and superspreading, which are critical to the spread and control of SARS-CoV-2.

Superspreading is one of the factors driving the transmission of various pathogens, including SARS-CoV-1, Middle Eastern respiratory syndrome coronavirus (MERS-CoV), and SARS-CoV-2. The number of secondary infections caused by one infectious person is subject to inter-individual variation. Heterogeneity in infectiousness or contact behavior is likely contributory in the superspreading events.

The SARS-CoV-2-infected population is more infectious during a certain, short period during which symptoms may not appear. Some people might infect more people because of increased contacts, or some might spread infections to a more vulnerable population despite having fewer contacts. Moreover, the environment plays an essential role in superspreading events; enclosed spaces are more prone to superspreading events than open or well-ventilated spaces.

The study

In the present study, researchers investigated the effect of different superspreading events on SARS-CoV-2 transmission in Belgium. Both infectiousness-related and contact-related heterogeneity were implemented in an individual-based model. A separate entity represents each individual with unique characteristics (age, behavioral traits, and health status) in this model.

The authors utilized an individual-based stochastic model termed simulator for the transmission of infectious diseases (STRIDE). This model was adapted to incorporate infectiousness-related and contact-related heterogeneity.

To account for infectiousness-related heterogeneity, an infected person is assigned with an ‘individual transmission probability,’ which determines whether the infection is transmitted to a susceptible person assuming that the probability remains constant throughout the infectious phase of the infected period.

A Gamma distribution represented inter-individual variation. Contact-related heterogeneity was implemented by multiplying the contact rate of an individual in the community and workplace by a factor drawn from the Gamma distribution. The authors performed about 200 stochastic simulations for superspreading events in the absence of external interventions (containment measures) and the presence of social distancing.

Superspreading simulation in the absence of interventions introduced one infected individual in a vulnerable community at the start of the simulation, observing the transmission for 200 days. In contrast, superspreading in the presence of social distancing introduced an infected person in a population for 30 days without interventions. Next, a lockdown period followed, marked by the closure of schools and fewer contacts in the workplace. After a lockdown of 60 days, restrictions were eased, allowing partial reopening.

Findings

The authors noted an increase in extinction probability with increased infectiousness-related heterogeneity. Extinction was observed in 12.5% of simulation runs in the baseline scenario (same transmission probability for all individuals). The final size of the outbreak was smaller when both infectiousness-related and contact-related heterogeneity was increased, particularly more with the increase in contact-related heterogeneity.

The mean epidemic peak decreased when the infectiousness-related heterogeneity was increased; conversely, it increased when contact-related heterogeneity was increased. Herd immunity threshold was attained much faster, and infections ceased much earlier with an increase in contact-related heterogeneity compared to infectiousness-related heterogeneity.

The effect of superspreading events was investigated considering the implementation of social distancing measures. In this case, outbreaks began explosively when contact-related heterogeneity was high. On the other hand, outbreaks ceased with only a few cases when high infectiousness-related heterogeneity was noted. During the lockdown, the number of cases dropped slightly with increasing infectiousness-related heterogeneity; however, they fell sharply after the partial release of lockdown.

High infectiousness-related heterogeneity in the partial relaxation phase was associated with a slower decline in outbreak. High contact-related heterogeneity was observed with more explosive outbreaks that were faster once the social distancing norms were eased. The researchers noted that social distancing had a limited impact on transmission.

Conclusions

In the absence of external containment measures with high infectiousness-related heterogeneity, introducing a single infected person resulted in less frequent outbreaks, and the herd immunity decreased. On the contrary, superspreading driven by infectiousness-related heterogeneity in a strict lockdown phase followed by partial relaxation almost effectively extinguished all outbreaks. However, in the case of superspreading driven by contact-related heterogeneity, infections remained limited during the strict lockdown phase but exploded following the relaxation of norms.

The simulations in the study assumed that each infected person eventually recovers and remains immune for the remainder of the simulation, and hence no deaths or reinfection were accounted for. Moreover, factors like immunity waning or vaccination were not modeled, making these observations representative of the first wave of the COVID-19 pandemic.

*Important notice

medRxiv publishes preliminary scientific reports that are not peer-reviewed and, therefore, should not be regarded as conclusive, guide clinical practice/health-related behavior, or treated as established information.

Written by

Tarun Sai Lomte

Tarun is a writer based in Hyderabad, India. He has a Master’s degree in Biotechnology from the University of Hyderabad and is enthusiastic about scientific research. He enjoys reading research papers and literature reviews and is passionate about writing.