The compartimental transmission model is one of the main models we use to model the transmission of infectious diseases. It divides the population into several conceptual subpopulations or compartments into which each individual is assigned.

In its simplest form, such a model describes the dynamics between a group of susceptible (S: susceptible), exposed (E: exposed), infectious (I: infectious) and recovered (R: recovered or removed) individuals, which is why this type of model is referred to as a SEIR model. Flows from one compartment to the next are described by differential equations--expressing the dynamics and velocity of that flow.

The__ infection pressure λ(t) __is time-dependent and indicates how quickly a susceptible person is exposed to the infectious agent (e.g. a virus). The model parameters γ (gamma) and σ (sigma) indicate the rate at which an exposed person becomes infectious or subsequently recovers and can no longer transmit the pathogen.

Greater infection pressure implies that the average number of persons infected by a "typical" infected person will be greater throughout the infectious period. In other words, the infection pressure λ(t) depends on the number of infected persons at time t in the population and on the probability of infection on contact between an infected and a susceptible person.

The compartmental models that we use to map the spread of COVID-19, however, are a lot more complex than this basic SEIR model. In addition to defining a group of exposed persons, the model includes a pre-symptomatic phase during which a person may be infectious before developing symptoms or before a formal diagnosis is conclusive. In addition, the model takes into account asymptomatic cases that also contribute to the further spread of the disease especially when they are unaware they are infectious. Unfortunately, in the case of COVID-19, additional compartments are needed besides recovery for everyone who is hospitalized and for those who eventually die.

The SEIR model then immediately looks a lot more complex:

After infection with SARS-CoV-2, a susceptible (S) person shifts to an exposed (E) status. As soon as they subsequently become infectious themselves, they belong to a pre-symptomatic category (I presym); both E and Ipresymp include the incubation period between which a person is already infected but does not (yet) show symptoms. Some will remain asymptomatic (I asym); others will develop mild (I mild) or severe (I sev) symptoms.

Those without symptoms and those whose symptoms remain mild will at some point recover (Recovered). If symptoms do become more severe, hospitalization (I hosp), perhaps even intensive care (I icu), is required, with two possible outcomes: recovery (Recovered) or death (Death).

The compartmental transmission model for COVID-19 not only contains more compartments than the basic SEIR model, but the flow between each is also more complex. Indeed, we consider movements from one compartment to another not only in function of time, but also in function of people's age and contact behavior. The distribution of the number of people by age group and the age-specific mortality of COVID-19 are taken into account in order to make realistic and correct short- and medium-term forecasts. Data from blood analyses are also included in the model in order to correct for those who have already been exposed to the virus in the past and are therefore not or less susceptible to a new infection.

The compartmental transmission model is a stochastic model. It allows real-time modeling and also lends itself to long-term projections (although, of course, the predictive value is highly dependent on how behaviors and measures vary), which is important, for example, in order to know how much medical supplies we should keep in stock. Of course, the model must be constantly updated with new data and better insights in order to adjust for variation and possible incorrect assumptions.

hospitalized patients▼

Even if the model is complex enough to take all sorts of factors into account, the result obviously stands or falls with the quality of the data we feed into the model. Garbage in, garbage out.

The more we know about the disease course and virus spread, the better and more realistic the models. In early versions of our compartmental transmission model for COVID-19, presymptomatic or asymptotic individuals are viewed as equally infectious as people with mild or severe symptoms, at least, before possible hospitalization (the model assumes that people in the hospital no longer spread the virus to others). It is not unlikely that people with severe symptoms have more virus particles in their airways and are more infectious, but we simply did not have good data to account for this in the model. At the same time, the more severe the symptoms, the more likely it is that a person will reduce his or her contacts, possibly compensating for the higher infectivity.

The model does take into account a difference in how long a person is infectious without symptoms, with mild symptoms or with severe symptoms, albeit via an approximation, namely the average time before a person is isolated or hospitalized, and thus the virus will not spread further. Although the model is able to account for differences in age-specific mortality between intensive care and other wards, or for example in residential care centers, they were initially considered the same, in the absence of more detailed figures. Important factors such as seasonal effects were also still a big question mark, and new insights on the SARS-CoV-2 virus and COVID-19 will allow for continued refinement of the model in the coming months and years.

Epidemiology & Infection,December 17, 2021

Phenomenological models are popular for describing the epidemic curve. We present how they can be used at different phases in the epidemic, by modelling the daily number of new hospitalisations (or cases). As real-time prediction of the hospital capacity is important, a joint model of the new hospitalisations, number of patients in hospital and in intensive care unit (ICU) is proposed. This model allows estimation of the length of stay in hospital and ICU, even if no (or limited) individual level information on length of stay is available. Estimation is done in a Bayesian framework. In this framework, real-time alarms, defined as the probability of exceeding hospital capacity, can be easily derived. The methods are illustrated using data from the COVID-19 pandemic in March–June 2020 in Belgium, but are widely applicable.