Complex network model for COVID-19: human behavior, pseudo-periodic solutions and multiple epidemic waves

TL;DR

This paper develops a complex network model incorporating human behavior and public health policies to explain multiple COVID-19 epidemic waves, demonstrating pseudo-periodic solutions and analyzing regional mobility impacts.

Contribution

It introduces a novel complex network model with piecewise constant parameters capturing behavioral effects and epidemic waves, supported by stability analysis and real data simulations.

Findings

Pseudo-oscillations between disease-free and endemic states explain epidemic waves.

Network topology influences infection levels and outbreak management.

Model provides a tool for regional outbreak control and border policy decisions.

Abstract

We propose a mathematical model for the transmission dynamics of SARS-CoV-2 in a homogeneously mixing non constant population, and generalize it to a model where the parameters are given by piecewise constant functions. This allows us to model the human behavior and the impact of public health policies on the dynamics of the curve of active infected individuals during a COVID-19 epidemic outbreak. After proving the existence and global asymptotic stability of the disease-free and endemic equilibrium points of the model with constant parameters, we consider a family of Cauchy problems, with piecewise constant parameters, and prove the existence of pseudo-oscillations between a neighborhood of the disease-free equilibrium and a neighborhood of the endemic equilibrium, in a biologically feasible region. In the context of the COVID-19 pandemic, this pseudo-periodic solutions are related to the emergence of epidemic waves. Then, to capture the impact of mobility in the dynamics of COVID-19 epidemics, we propose a complex network with six distinct regions based on COVID-19 real data from Portugal. We perform numerical simulations for the complex network model, where the objective is to determine a topology that minimizes the level of active infected individuals and the existence of topologies that are likely to worsen the level of infection. We claim that this methodology is a tool with enormous potential in the current pandemic context, and can be applied in the management of outbreaks (in regional terms) but also to manage the opening/closing of borders.