Miranda, José Garcia Vivas Silva, Mateus Souza Bertolino, José Gabriel Vasconcelos, Rodrigo Nogueira Cambui, Elaine Cristina Barbosa Araújo, Marcio Luis Valença Saba, Hugo Costa, Diego Pereira Duverger, Soltan Galano Oliveira, Matheus Teles de
...
Published in
Physica D. Nonlinear phenomena
The new Covid-19 pandemic has left traces of suffering and devastation to individuals of almost all countries worldwide and severe impact on the global economy. Understanding the clinical characteristics, interactions with the environment, and the variables that favor or hinder its dissemination help the public authorities in the fight and preventi...
Vyasarayani, C P Chatterjee, Anindya
Published in
Physica D. Nonlinear phenomena
We study an SEIQR (Susceptible-Exposed-Infectious-Quarantined-Recovered) model due to Young et al. (2019) for an infectious disease, with time delays for latency and an asymptomatic phase. For fast pandemics where nobody has prior immunity and everyone has immunity after recovery, the SEIQR model decouples into two nonlinear delay differential equa...
Comunian, Alessandro Gaburro, Romina Giudici, Mauro
Published in
Physica D. Nonlinear phenomena
Calibration of a SIR (Susceptibles-Infected-Recovered) model with official international data for the COVID-19 pandemics provides a good example of the difficulties inherent in the solution of inverse problems. Inverse modeling is set up in a framework of discrete inverse problems, which explicitly considers the role and the relevance of data. Toge...
Neves, Armando G M Guerrero, Gustavo
Published in
Physica D. Nonlinear phenomena
The presence of a large number of infected individuals with few or no symptoms is an important epidemiological difficulty and the main mathematical feature of COVID-19. The A-SIR model, i.e. a SIR (Susceptible-Infected-Removed) model with a compartment for infected individuals with no symptoms or few symptoms was proposed by Gaeta (2020). In this p...
Ballesteros, Angel Blasco, Alfonso Gutierrez-Sagredo, Ivan
Published in
Physica D. Nonlinear phenomena
Any epidemiological compartmental model with constant population is shown to be a Hamiltonian dynamical system in which the total population plays the role of the Hamiltonian function. Moreover, some particular cases within this large class of models are shown to be bi-Hamiltonian. New interacting compartmental models among different populations, w...
Beare, Brendan K Toda, Alexis Akira
Published in
Physica D. Nonlinear phenomena
The first confirmed case of Coronavirus Disease 2019 (COVID-19) in the US was reported on January 21, 2020. By the end of March, 2020, there were more than 180,000 confirmed cases in the US, distributed across more than 2000 counties. We find that the right tail of this distribution exhibits a power law, with Pareto exponent close to one. We invest...
James, Nick Menzies, Max Azizi, Lamiae Chan, Jennifer
Published in
Physica D. Nonlinear phenomena
This paper proposes a new method for determining similarity and anomalies between time series, most practically effective in large collections of (likely related) time series, by measuring distances between structural breaks within such a collection. We introduce a class of semi-metric distance measures, which we term MJ distances. These semi-metri...
Cadoni, Mariano Gaeta, Giuseppe
Published in
Physica D. Nonlinear phenomena
The most important features to assess the severity of an epidemic are its size and its timescale. We discuss these features in a systematic way in the context of SIR and SIR-type models. We investigate in detail how the size and timescale of the epidemic can be changed by acting on the parameters characterizing the model. Using these results and ha...
Weinstein, Steven J Holland, Morgan S Rogers, Kelly E Barlow, Nathaniel S
Published in
Physica D. Nonlinear phenomena
An analytic solution is obtained to the SEIR Epidemic Model. The solution is created by constructing a single second-order nonlinear differential equation in ln S and analytically continuing its divergent power series solution such that it matches the correct long-time exponential damping of the epidemic model. This is achieved through an asymptoti...
Li, Jeremiah Ye, Felix X. -F. Qian, Hong Huang, Sui
There is a growing awareness that catastrophic phenomena in biology and medicine can be mathematically represented in terms of saddle-node bifurcations. In particular, the term `tipping', or critical transition has in recent years entered the discourse of the general public in relation to ecology, medicine, and public health. The saddle-node bifurc...
