A New Compartmental Epidemiological Model for COVID-19 with a Case Study of Portugal
Ana P. Lemos-Paiao, Cristiana J. Silva, Delfim F. M. Torres
备注：
This is a preprint of a paper whose final and definite form is published by 'Ecological Complexity' (ISSN: 1476-945X). Paper Submitted 05/June/2020; Revised 24/July/2020, 08/Sept/2020 and 02/Nov/2020; Accepted 17/Nov/2020
We propose a compartmental mathematical model for the spread of the COVID-19 disease, showing its usefulness with respect to the pandemic in Portugal, from the first recorded case in the country till the end of the three states of emergency. New results include the compartmental model, described by a system of seven ordinary differential equations; proof of positivity and boundedness of solutions; investigation of equilibrium points and their stability analysis; computation of the basic reproduction number; and numerical simulations with official real data from the Portuguese health authorities. Besides completely new, the proposed model allows to describe quite well the spread of COVID-19 in Portugal, fitting simultaneously not only the number of active infected individuals but also the number of hospitalized individuals, respectively with a $L^2$ error of $9.2152e-04$ and $1.6136e-04$ with respect to the initial population. Such results are very important, from a practical point of view, and far from trivial from a mathematical perspective. Moreover, the obtained value for the basic reproduction number is in agreement with the one given by the Portuguese authorities at the end of the emergency states.
In [Ecological Complexity 44 (2020) Art. 100885, DOI: 10.1016/j.ecocom.2020.100885] a continuous-time compartmental mathematical model for the spread of the Coronavirus disease 2019 (COVID-19) is presented with Portugal as case study, from 2 March to 4 May 2020, and the local stability of the Disease Free Equilibrium (DFE) is analysed. Here, we propose an analogous discrete-time model and, using a suitable Lyapunov function, we prove the global stability of the DFE point. Using COVID-19 real data, we show, through numerical simulations, the consistence of the obtained theoretical results.
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, which are endowed with a Hamiltonian structure, are introduced. The Poisson structures underlying the Hamiltonian description of all these dynamical systems are explicitly presented, and their associated Casimir functions are shown to provide an effic…
In this work, we adapt the epidemiological SIR model to study the evolution of the dissemination of COVID-19 in Germany and Brazil (nationally, in the State of Paraiba, and in the City of Campina Grande). We prove the well posedness and the continuous dependence of the model dynamics on its parameters. We also propose a simple probabilistic method for the evolution of the active cases that is instrumental for the automatic estimation of parameters of the epidemiological model. We obtained statistical estimates of the active cases based the probabilistic method and on the confirmed cases data. …
Nowcasting and forecasting of epidemic spreading rely on incidence series of reported cases to derive the fundamental epidemiological parameters for a given pathogen. Two relevant drawbacks for predictions are the unknown fractions of undocumented cases and levels of nonpharmacological interventions, which span highly heterogeneously across different places and times. We describe a simple data-driven approach using a compartmental model including asymptomatic and presymptomatic contagions that allows to estimate both the level of undocumented infections and the value of effective reproductive …
A fractional compartmental mathematical model for the spread of the COVID-19 disease is proposed. Special focus has been done on the transmissibility of super-spreaders individuals. Numerical simulations are shown for data of Galicia, Spain, and Portugal. For each region, the order of the Caputo derivative takes a different value, that is not close to one, showing the relevance of considering fractional models.
We present a compartmental meta-population model for the spread of Covid-19 in India. Our model simulates populations at a district or state level using an epidemiological model that is appropriate to Covid-19. Different districts are connected by a transportation matrix developed using available census data. We introduce uncertainties in the testing rates into the model that takes into account the disparate responses of the different states to the epidemic and also factors in the state of the public healthcare system. Our model allows us to generate qualitative projections of Covid-19 spread …
A fractional-order compartmental model was recently used to describe real data of the first wave of the COVID-19 pandemic in Portugal [Chaos Solitons Fractals 144 (2021), Art. 110652]. Here, we modify that model in order to correct time dimensions and use it to investigate the third wave of COVID-19 that occurred in Portugal from December 2020 to February 2021, and that has surpassed all previous waves, both in number and consequences. A new fractional optimal control problem is then formulated and solved, with vaccination and preventive measures as controls. A cost-effectiveness analysis is c…
The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into compartments and has assumptions about the nature and time rate of transfer from one compartment to another. Usually, they are composed of a system of ordinary differential equations (ODE's) in time. A class of such models considers the Susceptible, Exposed, Infected, Recovered, and Deceased populations, the SEIRD model. However, these models do not always account…
IMT School for Advanced Studies Lucca（卢cca高等研究院）；TREE-TOWER S.R.L.（TREE-TOWER有限责任公司）
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Approaching epidemiological dynamics of COVID-19 with physics-informed neural networks
Frankfurt Institute for Advanced Studies（法兰克福高等研究院）；Xidian-FIAS International Joint Research Center（西安电子科技大学-法兰克福高等研究院国际联合研究中心）；Institut für Theoretische Physik, Goethe Universität Frankfurt（法兰克福大学理论物理研究所）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI亥姆霍兹重离子研究中心）；Xidian University（西安电子科技大学）
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