Rethinking classical epidemiological modeling in light of COVID-19 pandemic

Epidemiological models have been indispensable in aiding our understanding of the unfolding coronavirus disease 2019 (COVID-19) pandemic. A team of international scientists has recently developed an epidemiological model to explore the impact of individual variation in susceptibility and infectivity on transmission dynamics of an infectious disease across inhomogeneous populations. The study is currently available on the medRxiv* preprint server.

Background

In epidemiology, classical models are mostly based on assumptions that all individuals in a given population are equally susceptible to a particular infection and have the same propensity to transmit the infection to others. However, these assumptions are not always reasonable for infectious diseases with vast variation in individual infectivity. In the recent global outbreak of COVID-19, a small number of infected individuals are believed to be responsible for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection to a large number of individuals. Thus, an accurate estimation of the pandemic outcome is not possible with these classical models.  

In the current study, the scientists specifically analyzed two distinct but related aspects of the virus transmission dynamics: superspreading events and superspreading individuals. The events that produce many COVID-19 cases are termed as superspreading events. Similarly, a small group of specific individuals who create many infection cases are termed as superspreading individuals. Specifically, they considered that a superspreader is always an individual, and not an event.

Inhomogeneity of a given population, which plays a significant role in infection transmission dynamics, may depend on several factors, including individual variation in viral shedding, droplet generating ability, and contact networks. Moreover, the variation in ventilation systems at a given event or venue can significantly impact the transmission dynamics. In this study, the scientists separately analyzed two parameters: susceptibility and infectivity. They then assessed the correlation between these parameters in modulating transmission dynamics.

According to classical epidemiological models (SIR model), there are three categories in a given population: susceptible (S), infected (I), and recovered (R) individuals. In this model, the infection rate is proportional to the number of interactions between infected and susceptible individuals. On the other hand, the recovery rate is proportional to the number of infected individuals.

To investigate the total number of infections, the scientists modified this model by considering that these parameters are different for different individuals. In other words, they considered that the infection rate is a product of individual susceptibility and infectivity. The final mathematical equation they derived indicates that the total proportion of individuals who have ever been infected at a given time is the sum of currently infected and recovered individuals.

Important observations

The mathematical analysis carried out in this study indicated that the differences in individual susceptibility and infectivity have a significant impact on the total number of infections (epidemic size) and that the actual epidemic size primarily depends on the degree of correlation between susceptibility and infectivity; a higher correlation is associated with larger epidemic size.

In general, the analysis revealed that wider distribution of susceptible and infected individuals is associated with lower epidemic size. According to the model, the final epidemic size cannot be predicted only on the basis of infectivity and susceptibility proportions. The distribution dynamics of these parameters also have a significant impact on the final epidemic size.

Regarding superspreading, the model revealed that the correlation between susceptibility and infectivity robustly influences the effects of superspreaders on the initial growth rate of the epidemic. By increasing the number of superspreaders without altering the average infectivity and susceptibility, the scientists observed an induction in the initial growth rate of the epidemic, which eventually increased the final epidemic size. In contrast, they observed a reduction in final epidemic size by adding one superspreader and one remarkably careful individual in the model. This adjustment was done to increase the individual variation.

In the current model, the scientists did not consider the option of reinfection. They believe that the impact of superspreaders on actual epidemic size would be much higher if reinfection of recovered individuals is considered in the model.

Study significance

The study provides an efficient mathematical model to evaluate the dynamics of transmission of an infectious disease for a population with differences in individual susceptibility and infectivity (inhomogeneous population). The findings reveal that in a given population, the differences in an individual’s ability to acquire and transmit the infection matters the most in shaping the outcome of an epidemic or a pandemic situation. Because the measurement of individual infectivity and susceptibility of many people is a prerequisite for determining the distribution dynamics, the scientists believe that predicting the final epidemic size is a difficult task in real life.

*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

Dr. Sanchari Sinha Dutta

Dr. Sanchari Sinha Dutta is a science communicator who believes in spreading the power of science in every corner of the world. She has a Bachelor of Science (B.Sc.) degree and a Master's of Science (M.Sc.) in biology and human physiology. Following her Master's degree, Sanchari went on to study a Ph.D. in human physiology. She has authored more than 10 original research articles, all of which have been published in world renowned international journals.