Analysis on stability of an autonomous dynamics system for sars epidemic

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Dynamics

Background:

• The SARS epidemic posed a significant global health threat.
• Understanding epidemic dynamics is crucial for effective public health interventions.
• Existing models may not fully capture complex population and disease factors.

Purpose of the Study:

• To develop an extended dynamic model for SARS epidemic.
• To incorporate susceptible population density constraints, cure, and death rates.
• To analyze the stability and persistence of the epidemic.

Main Methods:

• Deduction of an extended dynamic model based on the K-M infection model.
• Inclusion of density-dependent susceptible population dynamics.
• Analysis of infection-free and endemic equilibrium stability.

Main Results:

• The infection-free equilibrium was found to be globally asymptotically stable under specific conditions.
• The endemic equilibrium was determined to be not asymptotically stable.
• The model suggests permanent persistence of the epidemic system under appropriate conditions.

Conclusions:

• The extended model provides insights into SARS epidemic persistence.
• Population density and recovery rates significantly influence epidemic dynamics.
• The findings underscore the importance of sustained control strategies to manage persistent infectious diseases.