A multi-group SEIRA model for the spread of COVID-19 among heterogeneous populations

Abstract

The outbreak and propagation of COVID-19 have posed a considerable challenge to modern society. In particular, the different restrictive actions taken by governments to prevent the spread of the virus have changed the way humans interact and conceive interaction. Due to geographical, behavioral, or economic factors, different sub-groups among a population are more (or less) likely to interact, and thus to spread/acquire the virus. In this work, we present a general multi-group SEIRA model for representing the spread of COVID-19 among a heterogeneous population and test it in a numerical case of study. By highlighting its applicability and the ease with which its general formulation can be adapted to particular studies, we expect our model to lead us to a better understanding of the evolution of this pandemic and to better public-health policies to control it.

Keywords: COVID-19 pandemic; Multigroup model; Public-health; SARS-CoV2; SEIRA models.

Fig. 1

Our approach proposes the partition of a heterogeneous population into several (as-many-as-required) sub-populations, where the hypotheses for SEIR models are satisfied. The different populations share common characteristics, as a geographical zone (this scheme), but not restricted only to that interpretation. This same reasoning (and model) can be applied to different behavioral groups, social classes, and age groups, through an appropriate interpretation for the interaction function.

Fig. 2

Schematic representation of the contagion processes between classes. According to the form of the interaction matrix Φ, individuals from class i would contribute to the floating population of class j, where they would interact with individuals from -in principle- all other classes. As among them might be infected individuals from all origins, the interaction term should be corrected as presented.

Fig. 3

Schematic representation of the two interactive configurations between zones A, B, and C. Zone C has a working-dependency with zone A, and zone B acts as the middle point. This is a simplified version of a case observed in Santiago de Chile, where the outbreak was concentrated in the wealthiest part of the city, but quickly spread to zones where service providers live.

Fig. 4

Numeric simulations of cases 1-4, with outbreak parameters $\beta =0.11,$$\gamma =0.034,$$\theta =0.001,$$\xi =2,$$\alpha =0.3,$$n={10}^5\left[2.556\right],$${\beta }^q=0.044,$$I_A(t=0)=10$. Note that this simulation does not consider the saturation of the local health-system, a parameter that drastically increases the mortality rate of this virus when surpassed.