Dynamics of a non-smooth epidemic model with three thresholds

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• Infectious disease transmission is complex, influenced by factors like media coverage, vaccination, and treatment.
• Existing models may not fully capture dynamics influenced by the rate of change in case numbers and policy interventions.

Purpose of the Study:

• To propose and analyze a novel non-smooth epidemic model incorporating piecewise incidence rates.
• To investigate the impact of media coverage, vaccination, and treatment policies on disease dynamics.
• To determine conditions for disease containment and understand the role of policy thresholds.

Main Methods:

• Development of a non-smooth epidemic model with a piecewise incidence rate.
• Conversion of an implicitly defined system to an explicit system using the Lambert W function.
• Analysis of model dynamics, including generalized and pseudo-equilibria, for limiting cases.

Main Results:

• The model demonstrates that disease containment is achievable at different levels (a priori, high, or low) based on policy thresholds.
• Media coverage does not eradicate the disease but effectively delays the epidemic peak and reduces its magnitude.
• Policy implementation, governed by thresholds, dictates whether enhanced vaccination and treatment are activated.

Conclusions:

• Effective disease control requires a well-defined threshold policy for interventions.
• Continuous public awareness campaigns regarding case numbers are crucial for successful disease management.
• The model provides insights into optimizing public health strategies for infectious diseases.