Extensions of the SEIR Model for the Analysis of Tailored Social Distancing and Tracing Approaches to Cope with COVID-19

Abstract

In the context of the COVID-19 pandemic, governments worldwide face the challenge of designing tailored measures of epidemic control to provide reliable health protection while allowing more societal and economic activity. In this paper, we propose an extension of the epidemiological SEIR model to enable a detailed analysis of commonly discussed tailored measures of epidemic control-among them group-specific protection and the use of tracing apps. We introduce groups into the SEIR model that may differ both, in their underlying parameters as well as in their behavioral response to public health interventions. We allow for different infectiousness parameters within and across groups, different asymptomatic, hospitalization, and lethality rates, as well as different take-up rates of tracing apps. Our results visualize the sharp trade-offs between different goals of epidemic control, namely a low death toll, avoiding overload of the health system, and a short duration of the epidemic. We show that a combination of tailored mechanisms, e.g., the protection of vulnerable groups together with a "trace & isolate" approach, can be effective in preventing a high death toll. Protection of vulnerable groups without further measures requires unrealistically strict isolation. A key insight is that high compliance is critical for the effectiveness of a "trace & isolate" approach. Our model allows to analyze the interplay of group-specific social distancing and tracing also beyond our case study in scenarios with a large number of groups reflecting, e.g., sectoral, regional, or age differentiation and group-specific take-up rates for tracing apps.

On build‐up of epidemiologic models—Development of a SEI3RSD model for the spread of SARS‐CoV‐2

“…In Section 2.1.5, we deal with this item in detail. (ii)The specifics of an infection process are taken into account like mean duration of infectiousness of an individual, delay of infectiousness by a newly infected person (latent period), mean duration of acquired immunity after an overcome infection. Detailed explications are given in Section 2.2. (iii) Outer influences on the infection process are considered like vaccinations and their temporal delay after the begin of infection (see Paragraph 3.3), available capacities of intensive care or political measures to contain further infections, see for instance [21,22]. …”

“…Thus, they are aware of their disease and, therefore, they strongly change their contact behaviour or they are hospitalized. Sometimes, a further subdivision in parallel is performed, for instance, infectious persons (without symptoms) in quarantine can be considered, see [21]. (iii)The number of recovered persons is usually abbreviated by R and r , respectively.…”

“…However, to get a complete result, dead individuals should constitute an extra class. This is particularly the case, if the lethality is influenced by outer circumstances like availability of intensive‐care units in hospitals, see [21].…”

“…A small overview can be found in [3]. Moreover, we refer to [21]. Contrary to standard models, there the individual groups of persons like susceptible and infective ones are further subdivided to address specific moments in their behaviour.…”

“…I 3 means, that there are distinguished three classes of infectious persons. Contrary to [21] we only subdivide classes of population with respect to the course of infection and disease, but not with respect to age or social behaviour. However, the mentioned modular design principle allows to extend the model in case of necessity. (iii)In Section 4, we deal with some mathematical questions arising from the developed models.…”