A Discrete Model for the Evolution of Infection Prior to Symptom Onset

Jordi Ripoll

University of Girona, Spain

"A Discrete Model for the Evolution of Infection Prior to Symptom Onset"

We study the generation-time distribution, i.e. timing of infection events, in a discrete-time epidemic model with asymptomatic carriers. The progression of the disease is categorized into four phases: the non-infectious latent phase, the infectious asymptomatic phase (a key feature of the model where individuals exhibit mild or no symptoms), the infectious symptomatic phase, and lastly, the immune phase. We introduce a versatile non-Markovian system with generic waiting times at infected stages and transmission rates depending on the elapsed time since infection. The basic reproduction number is derived from a renewal equation for the (sequence of) asymptomatic hosts, whose expression gives the probability distribution of the time between new cases in a chain of infection transmission (generation time). For illustration purposes, we consider Weibull distributions which include both geometric and fixed-length distributions as particular cases. For memoryless waiting times (geometric distribution), we have investigated the evolution of infection transmission before and after symptom onset. Given that individuals can develop symptoms and die from the disease, we consider disease-induced mortality as a measure of virulence and assume it is positively correlated with a weighted average transmission rate. Our findings indicate that the infection transmission rate is consistently higher during the symptomatic phase. However, in some scenarios, the majority of infections occur prior to symptom onset. [1] A Discrete Model for the Evolution of Infection Prior to Symptom Onset, J. Ripoll and J. Font, Mathematics 2023, 11(5), 1092. [2] Generation time in a discrete epidemic model with asymptomatic carriers: beyond geometric waiting-times, J. Ripoll and J. Saldaña, IMAE-preprint.

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