A novel queue-based stochastic epidemic model with adaptive stabilising control.

Area of Science:

• Epidemiology
• Mathematical Modeling
• Stochastic Processes

Background:

• Traditional SEIR models often assume exponential distributions for disease latency and infectious periods.
• Generalizing these distributions is crucial for accurately modeling real-world epidemics.
• Existing generalized models can be complex and computationally intensive.

Purpose of the Study:

• To propose a novel stochastic SEIR epidemic model accommodating general latency and infectious period distributions.
• To develop a tractable mathematical framework for analyzing epidemic dynamics under these general distributions.
• To derive conditions for epidemic control and propose effective mitigation strategies.

Main Methods:

• Development of a novel SEIR stochastic epidemic model.
• Utilizing queuing systems with infinitely many servers and time-varying Markov chains.
• Derivation of a sufficient condition for epidemic shrinking based on stochastic stability and queuing system occupation rate.
• Design of stabilizing mitigation strategies targeting occupation rate balance.

Main Results:

• The proposed model is as tractable as previous models with exponential distributions.
• It is more straightforward than semi-Markov models with similar generality.
• A sufficient condition for epidemic control was derived based on the queuing system's occupation rate.
• The model and strategies were validated using COVID-19 data from England and Amazonas, Brazil.

Conclusions:

• The novel SEIR model provides a tractable yet general framework for epidemic modeling.
• Timely implemented mitigation strategies can effectively curb epidemic spread by managing the queuing system's occupation rate.
• The approach shows promise for controlling epidemics like COVID-19.