Stochastic COVID-19 SEIQ epidemic model with time-delay

Area of Science:

• Epidemiology
• Mathematical Biology
• Stochastic Processes

Background:

• The COVID-19 pandemic highlighted the need for robust epidemic models.
• Understanding the impact of random fluctuations and time delays is crucial for disease control.

Purpose of the Study:

• To develop and analyze a stochastic epidemic model for COVID-19.
• To investigate the existence and uniqueness of solutions in a feasible region.
• To establish conditions for disease extinction.

Main Methods:

• A four-class epidemic model (Susceptible, Exposed, Infectious, Quarantine) was formulated.
• Lyapunov functions were applied within a delay-stochastic framework.
• Numerical simulations were performed for model validation.

Main Results:

• The existence of at least one unique non-local solution was proven.
• Conditions for the extinction of COVID-19 were established.
• Brownian motion and noise terms were found to have a significant effect on transmission.

Conclusions:

• Stochastic perturbations can play a critical role in epidemic dynamics.
• Higher noise levels may lead to a reduction or disappearance of infections.
• The model provides insights into controlling COVID-19 spread through managing uncertainty.