Effect of time-dependent infectiousness on epidemic dynamics

TL;DR

This paper investigates how incorporating time-dependent infectiousness, based on viral load, affects epidemic dynamics and reproductive numbers, revealing significant impacts on epidemic peak timing and behavior.

Contribution

It introduces a model with time-dependent infectiousness and compares it to the standard SIR model, highlighting differences in epidemic progression and reproductive number dependencies.

Findings

Reproductive number depends on total infectious exposure and mixing matrix eigenvalues.

Time-dependent model predicts an earlier epidemic peak than the standard SIR model.

Infectiousness transition creates wave-like epidemic behavior.

Abstract

In contrast to the common assumption in epidemic models that the rate of infection between individuals is constant, in reality, an individual's viral load determines their infectiousness. We compare the average and individual reproductive numbers and epidemic dynamics for a model incorporating time-dependent infectiousness and a standard SIR model for both fully-mixed and category-mixed populations. We find that the reproductive number only depends on the total infectious exposure and the largest eigenvalue of the mixing matrix and that these two effects are independent of each other. When we compare our time-dependent mean-field model to the SIR model with equivalent rates, the epidemic peak is advanced and modifying the infection rate function has a strong effect on the time dynamics of the epidemic. We also observe behavior akin to a traveling wave as individuals transition through infectious states.