Epidemic models with heterogeneous mixing and indirect transmission

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• Traditional epidemic models often assume direct contact for pathogen transmission.
• Understanding indirect transmission routes and virus shedding is crucial for accurate disease spread prediction.
• Heterogeneous mixing patterns significantly influence epidemic dynamics.

Purpose of the Study:

• To develop an age of infection model that incorporates indirect transmission and virus shedding.
• To analyze the impact of population mixing and patch connectivity on disease spread.
• To evaluate the potential for disease invasion using mathematical modeling.

Main Methods:

• Development of a novel age of infection model based on the SIRP (Susceptible-Infectious-Recovered-Progeny) epidemic model.
• Incorporation of virus shedding as a function of the age of infection.
• Mathematical analysis including computation of the basic reproduction number, initial exponential growth rate, and final size relation.
• Modeling a two-patch SIRP system to assess the influence of patch connection and environmental factors.

Main Results:

• The age of infection model provides a framework for understanding indirect transmission dynamics.
• Virus shedding rates are shown to be dependent on the age of infection, influencing transmission.
• Mathematical analysis reveals the impact of patch connectivity on epidemic spread and invasion potential.
• The final size relation is utilized to assess short-term disease invasion capabilities.

Conclusions:

• The developed age of infection model offers a more nuanced approach to studying epidemic spread.
• Indirect transmission and age-dependent virus shedding are important factors in disease dynamics.
• Population structure and connectivity play a significant role in disease invasion and persistence.
• Mathematical modeling provides valuable insights into predicting and managing infectious disease outbreaks.