In this work, we consider an epidemiological model given by a system of ordinary equations, for the transmission dynamics of SARS-CoV-2, with piecewise constant parameters. Based on this model, we construct a complex network of dynamical systems, in order to take into account the mobilities of individuals, which are known to play a decisive role in the dynamics of the epidemic.
We prove the existence of pseudo-periodic solutions of the epidemic model and analyze its relation with multiple epidemic waves in COVID-19 pandemic.
Our model is calibrated in order to fit with the real data of the COVID-19 active infected individuals in six regions of Portugal mainland, namely Norte, Centro, Lisboa e Vale do Tejo, Alentejo, Algarve and Pinhal Litoral.
Through numerical simulations, we explore the effect of the topology of the network on the dynamics of the epidemics (disposal of connections and coupling strength) and identify which type of topology minimizes the level of infection of the epidemic.

This is a joint work with Guillaume Cantin, Carla Cruz, Rui Fonseca-Pinto, Rui Passadouro da Fonseca, Estevão Soares dos Santos and Delfim F. M. Torres, developed under the project Project Nr.147 "Controlo Ótimo e Modelação Matemática da Pandemia COVID-19:
contributos para uma estratégia sistémica de intervenção em saúde na comunidade", in the scope of the "RESEARCH 4 COVID-19" call, financed by the Portuguese Foundation for Science and Technology (FCT),  see [1],[2]. 

References:

[1] Cristiana J. Silva, Guillaume Cantin, Carla Cruz, Rui Fonseca-Pinto, Rui Passadouro da Fonseca, Estevão Soares dos Santos, Delfim F. M. Torres, Complex network model for COVID-19: human behavior, pseudo-periodic solutions and multiple epidemic waves, submitted.
https://arxiv.org/abs/2010.02368

[2] Cristiana J. Silva, Carla Cruz, Delfim F. M. Torres, Alberto P. Munuzuri, Alejandro Carballosa, Iván Area, Juan J. Nieto, Rui Fonseca-Pinto, Rui Passadouro da Fonseca, Estevão Soares dos Santos, Wilson Abreu, Jorge Mira, Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal, submitted. https://arxiv.org/abs/2009.00660