Effect of time-dependent infectiousness on epidemic dynamics

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• Standard epidemic models often assume constant infection rates.
• Individual infectiousness varies based on factors like viral load.
• This variability is crucial for accurate epidemic prediction.

Purpose of the Study:

• To compare epidemic dynamics using a time-dependent infectiousness model versus a standard SIR model.
• To analyze how individual viral load influences infectiousness and overall epidemic spread.
• To investigate the impact of population mixing on epidemic outcomes.

Main Methods:

• Developed a mean-field epidemic model with time-dependent infectiousness.
• Compared this model to the standard Susceptible-Infected-Recovered (SIR) model.
• Analyzed both fully mixed and category-mixed population structures.

Main Results:

• Reproductive number depends independently on total infectious exposure and mixing matrix eigenvalue.
• Time-dependent infectiousness advances the epidemic peak compared to standard SIR models.
• Modifying infection rate functions significantly alters epidemic time dynamics, showing traveling wave-like behavior.

Conclusions:

• Individual viral load is a critical factor in epidemic modeling, not just average rates.
• Time-dependent infectiousness models provide more realistic epidemic dynamics.
• Population structure and individual infectiousness interact to shape epidemic trajectories.