An age-of-infection model with both symptomatic and asymptomatic infections

TL;DR

This paper develops a comprehensive age-of-infection epidemic model incorporating symptomatic and asymptomatic pathways, calculates key epidemiological metrics, and analyzes the final epidemic size with numerical validation.

Contribution

It introduces a general age-of-infection model with dual infection pathways and derives analytical expressions for the basic reproduction number and final size relations.

Findings

The ratio of symptomatic to asymptomatic cases depends on the symptomatic ratio f.

Final size bounds are established for epidemics with disease deaths.

Numerical simulations confirm the analytical results.

Abstract

We formulate a general age-of-infection epidemic model with two pathways: the symptomatic infections and the asymptomatic infections. We then calculate the basic reproduction number $\mathcal{R}_0$ and establish the final size relation. It is shown that the ratio of accumulated counts of symptomatic patients and asymptomatic patients is determined by the symptomatic ratio $f$ which is defined as the probability of eventually becoming symptomatic after being infected. We also formulate and study a general age-of-infection model with disease deaths and with two infection pathways. The final size relation is investigated, and the upper and lower bounds for final epidemic size are given. Several numerical simulations are performed to verify the analytical results.