Seir epidemiological model with varying infectivity and infinite delay

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• Understanding disease dynamics is crucial for public health interventions.
• Age-dependent infectivity and delays significantly impact disease transmission patterns.
• Existing models may not fully capture complex transmission dynamics.

Purpose of the Study:

• To develop a new Susceptible-Exposed-Infectious-Recovered (SEIR) model incorporating distributed infinite delay.
• To analyze the influence of age-dependent infectivity on disease spread.
• To determine the conditions for disease persistence or eradication using mathematical modeling.

Main Methods:

• Derivation of a novel SEIR model with distributed infinite delay.
• Calculation of the basic reproduction number (R0) as a critical threshold.
• Application of a permanence theorem for infinite dimensional systems to analyze long-term disease behavior.

Main Results:

• The disease-free equilibrium is globally asymptotically stable when R0 < 1.
• An endemic equilibrium, locally asymptotically stable, emerges when R0 > 1.
• The disease is shown to be persistent when R0 > 1, indicating endemicity.

Conclusions:

• The derived SEIR model provides a framework for studying diseases with age-dependent infectivity and delays.
• The basic reproduction number (R0) effectively predicts disease-free or endemic states.
• Mathematical analysis confirms disease persistence under specific conditions (R0 > 1).