Vaccine impact in homogeneous and age-structured models

Area of Science:

• Epidemiology
• Mathematical Modeling
• Vaccinology

Background:

• Childhood diseases necessitate effective vaccination strategies.
• Imperfect vaccines, characterized by various failure modes, present unique challenges in disease control.
• Understanding vaccine failure mechanisms is crucial for accurate transmission modeling.

Purpose of the Study:

• To develop a general mathematical model for imperfect childhood vaccines.
• To investigate the impact of different vaccine failure types on disease transmission.
• To compare transmission dynamics in homogeneous versus age-specific population mixing models.

Main Methods:

• Extended standard SEIR (Susceptible-Exposed-Infectious-Recovered) equations to include a vaccinated compartment.
• Incorporated five vaccine parameters: "leakiness," "all-or-nothingness," waning immunity, reduced infectiousness, and reduced reporting probability.
• Analyzed disease transmission using both homogeneous and age-specific mixing models, deriving analytic expressions for age-specific vaccine impacts.

Main Results:

• Vaccine failures related to susceptibility (leakiness, all-or-nothingness, waning) and reduced infectiousness significantly affect disease transmission (basic reproduction number).
• Vaccine impact on transmission differs between homogeneous and age-structured models.
• Waning vaccine protection can lead to greater transmission reduction in age-structured models with specific contact patterns between age groups.

Conclusions:

• The study provides a framework for understanding imperfect vaccine dynamics in childhood disease transmission.
• Age-specific contact structures are critical for accurately assessing the impact of waning vaccine immunity.
• Overall vaccine impact is constrained by the age-specific impacts across different population segments.