Why Not Every Contact Leads to Illness express
Ordinary models assume that infection is like a steady flow of water that washes over everyone equally. In reality, the stream from a sick person fluctuates: right after infection it barely trickles, then turns into a raging downpour, and later subsides. The chance of catching the virus depends on the strength of this flow at the moment of contact.
The new model describes this unpredictability through the 'age of infection'—the number of days since infection. Scientists broke down the dynamics of contagiousness into time segments, and using Markov's ideas about random transitions, they created vivid forecasts. It turned out to be all about the spread of the virus and the dose received.
This explains why sometimes in a crowded bus no one gets infected, while a fleeting conversation leads to illness: it's not the meeting that matters, but the dose and timing.
Original abstract
as written by the authors arXiv:2607.15104
We explore a model of infectious disease spread that incorporates exposure to the pathogen in the classic epidemiological acceptation of the term, i.e., a contact with an infectious individual has taken place but the infection has not necessarily been acquired. The model also includes a (discrete) age of infection structure, allowing to implicitly describe the viral load of infected individuals and in turn, to describe the probability of developing an infection as a function of the viral load of the infectious contacts.
For many viruses, the peak of contagiousness occurs before symptoms appear, so a person may not suspect they are already spreading the infection.