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Complex network model for COVID-19: human behavior, pseudo-periodic solutions and multiple epidemic waves
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Abstract(s)
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.
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Citation
Silva, Cristiana & Guillaume, CANTIN & Cruz, Carla & Fonseca-Pinto, Rui & Passadouro, Rui & Soares dos Santos, Estevão & Torres, Delfim F. M.. (2021). Complex network model for COVID-19: Human behavior, pseudo-periodic solutions and multiple epidemic waves. Journal of Mathematical Analysis and Applications. 125171. 10.1016/j.jmaa.2021.125171.