COVID-19 Dynamics: A Heterogeneous Model

Abstract

The mathematical model reported here describes the dynamics of the ongoing coronavirus disease 2019 (COVID-19) epidemic, which is different in many aspects from the previous severe acute respiratory syndrome (SARS) epidemic. We developed this model when the COVID-19 epidemic was at its early phase. We reasoned that, with our model, the effects of different measures could be assessed for infection control. Unlike the homogeneous models, our model accounts for human population heterogeneity, where subpopulations (e.g., age groups) have different infection risks. The heterogeneous model estimates several characteristics of the epidemic more accurately compared to the homogeneous models. According to our analysis, the total number of infections and their peak number are lower compared to the assessment with the homogeneous models. Furthermore, the early-stage infection increase is little changed when population heterogeneity is considered, whereas the late-stage infection decrease slows. The model predicts that the anti-epidemic measures, like the ones undertaken in China and the rest of the world, decrease the basic reproductive number but do not result in the development of a sufficient collective immunity, which poses a risk of a second wave. More recent developments confirmed our conclusion that the epidemic has a high likelihood to restart after the quarantine measures are lifted.

A note on variable susceptibility, the herd-immunity threshold and modeling of infectious diseases

“…It is a very curious fact that the division of S into subcompartments can not, in contrast to I, mathematically be further reduced to a simpler equation system. However, and this is the key result of this paper, we can prove mathematically that the overall behavior of S-SIR (in terms of prevalence I and recovered R) differs only marginally from the basic SIR ( 3)-( 4) upon including ASI to the initial conditions, as we did in (5). This is the essence of Theorem 2.1, which is found in SM Section 2.…”

“…Ch. 1 and 3 in [4], and the articles [5][6][7][8]. Similar results have also been established numerically for other heterogeneities, such as age and activity [9].…”

The role of super-spreaders in modeling of SARS-CoV-2

“…There are various papers studying numerically how various population heterogeneities affect the model curves, with the result that most heterogeneities such as variation in social activity or susceptibility, does have a damping effect on the overall spread ( Britton et al, 2020 ; Dolbeault & Turinici, 2021 ; Gerasimov et al, 2021 ). From this perspective, the finding that variable infectivity does not affect model output is a bit surprising.…”

Modeling complex systems: A case study of compartmental models in epidemiology

“…Therefore, in this section we will discuss the widely used assumption of homogeneous and well-mixed populations [25][26][27][28]36]. The homogeneity assumption has been challenged using various types of heterogeneous models [12,[40][41][42][43][44], and these studies point towards a crucial result: heterogeneous models can yield very different outcomes from homogeneous models.…”

“…To summarize this impact of heterogeneous infectiousness, susceptibility, and connectivity, we use a simple class of models in which the population is partitioned into multiple groups [12,[40][41][42][43][44]. We briefly describe these models below (methods can be found in Appendix section 4).…”