Deterministic and stochastic models for the epidemic dynamics of COVID-19 in Wuhan, China
Autor: | Xueying Wang, Angela Tower, Damilola Olabode, Jordan Culp, Allison Fisher, Dylan Hull-Nye |
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Rok vydání: | 2021 |
Předmět: |
disease outbreak
China Time Factors Stochastic modelling ctmc model lcsh:Biotechnology Basic Reproduction Number 02 engineering and technology lcsh:TP248.13-248.65 0502 economics and business 0202 electrical engineering electronic engineering information engineering Applied mathematics Humans Epidemics Pandemics Branching process Mathematics Probability Stochastic Processes Markov chain Stochastic process SARS-CoV-2 lcsh:Mathematics Applied Mathematics 05 social sciences seir model Ode COVID-19 ode model General Medicine Models Theoretical lcsh:QA1-939 second wave Markov Chains disease extinction Computational Mathematics Nonlinear system Modeling and Simulation Ordinary differential equation 020201 artificial intelligence & image processing General Agricultural and Biological Sciences Constant (mathematics) 050203 business & management |
Zdroj: | Mathematical Biosciences and Engineering, Vol 18, Iss 1, Pp 950-967 (2021) |
ISSN: | 1551-0018 |
Popis: | In this paper, deterministic and stochastic models are proposed to study the transmission dynamics of the Coronavirus Disease 2019 (COVID-19) in Wuhan, China. The deterministic model is formulated by a system of ordinary differential equations (ODEs) that is built upon the classical SEIR framework. The stochastic model is formulated by a continuous-time Markov chain (CTMC) that is derived based on the ODE model with constant parameters. The nonlinear CTMC model is approximated by a multitype branching process to obtain an analytical estimate for the probability of a disease outbreak. The local and global dynamics of the disease are analyzed by using the deterministic model with constant parameters, and the result indicates that the basic reproduction number $ \mathcal{R}_0 $ serves as a sharp disease threshold: the disease dies out if $ \mathcal{R}_0\le 1 $ and persists if $ \mathcal{R}_0 > 1 $. In contrast to the deterministic dynamics, the stochastic dynamics indicate that the disease may not persist when $ \mathcal{R}_0 > 1 $. Parameter estimation and validation are performed to fit our ODE model to the public reported data. Our result indicates that both the exposed and infected classes play an important role in shaping the epidemic dynamics of COVID-19 in Wuhan, China. In addition, numerical simulations indicate that a second wave of the ongoing pandemic is likely to occur if the prevention and control strategies are not implemented properly. |
Databáze: | OpenAIRE |
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