The dynamical model for COVID-19 with asymptotic analysis and numerical implementations.

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• The 2019 novel coronavirus (COVID-19) has caused a global pandemic with significant health and societal impacts.
• Understanding COVID-19 transmission dynamics is crucial for effective control strategies.
• Factors such as isolation, diagnosis, recovery, and mortality rates influence disease spread.

Purpose of the Study:

• To develop and analyze a mathematical model for COVID-19 transmission.
• To investigate the impact of various factors, including isolation and infection rates, on disease spread.
• To validate the model using clinical data from Wuhan and Italy.

Main Methods:

• Establishment of a mathematical model incorporating imported cases, isolation, diagnosis, recovery, and mortality rates.
• Assumption of Weibull distribution for incubation, cure, and diagnosis periods.
• Analysis using a linear integral-differential equation with a convolution kernel.
• Asymptotic behavior analysis and quantitative assessment of the model.

Main Results:

• Rigorous proof that infected patient numbers and their variation ratio tend to zero under sufficient isolation or low infection rates.
• Demonstration of the model's validity through numerical simulations.
• Comparison of model simulations with clinical data from Wuhan and Italy.

Conclusions:

• Effective isolation measures and low infection rates are critical for controlling COVID-19 spread.
• The developed mathematical model accurately reflects COVID-19 transmission dynamics.
• The model provides a valuable tool for understanding and predicting pandemic trajectories.