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
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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