Lifting Lockdown Control Measure Assessment: From Finite to Infinite-dimensional Epidemic Models for COVID-19

TL;DR

This paper develops and compares various advanced epidemic models for COVID-19, incorporating factors like age structure, delays, and in-host dynamics, to better understand and evaluate control measures for lifting lockdowns.

Contribution

It introduces a hierarchy of COVID-19 models from basic to complex, integrating age, delay, and demographic effects, with rigorous bifurcation analysis.

Findings

Models reveal the impact of latency periods on disease severity.

Age-structure influences transmission dynamics significantly.

Bifurcation analysis identifies critical factors for disease progression.

Abstract

The main focus of this chapter is on public health control strategies which are currently the main way to mitigate COVID-19 pandemic. We introduce and compare compartmental models of increasing complexity for COVID-19 transmission to describe dynamics of the disease spread. We begin by considering an SEAIR model including basic characteristics related to COVID-19. Next, we shall pay attention to age-structure modeling to emphasis the role of age-group individuals on the disease spread. A Model with constant delay is also formulated to show the impact of the latency period on the severity of COVID-19. Since there is evidence that for COVID-19 disease, important relationships exist between what is happening in the host and what is occurring at the population level, we shall link the basic model to in-host dynamics through the so-called threshold-type delay models. Finally, we will include demographic effects to the most complex models and we will conduct rigorous bifurcation analysis to quantify possible factors responsible for disease progression.