Year: 2025
Type: article
Abstract: We consider a model for the spread of an influenza-like disease in which, between seasons, the virus makes a random genetic drift (reducing immunity) and obtains a new random transmissibility (closely related to $$R_0$$ R 0 ). Given the immunity status at the start of season k , i.e. the community distribution of years since last infection and their associated immunity levels, the outcome of the epidemic season k , characterized by the effective reproduction number $$R_e^{(k)}$$ R e ( k ) and the fractions infected in the different immunity groups $${\textbf {z}}^{(k)}$$ z ( k ) , is determined by the random genetic drift and transmissibility. It is shown that the community immunity status of consecutive seasons, is an ergodic Markov chain, which converges to a stationary distribution. More analytical progress is made for the case where immunity only lasts for one season: we then characterize the stationary distribution of the community fraction having partial immunity (from being infected last season) as well as the stationary distribution of $$(R_e^{(k)}, z^{(k)})$$ ( R e ( k ) , z ( k ) ) , and the conditional distribution of $$z^{(k)}$$ z ( k ) given $$R_e^{(k)}$$ R e ( k ) . The effective reproduction number $$R_e^{(k)}$$ R e ( k ) is closely related to the initial exponential growth rate $$\rho ^{(k)}$$ ρ ( k ) of the outbreak, a quantity which can be estimated early in the epidemic season. As a consequence, this conditional distribution may be used for predicting the final size of the epidemic based on its initial growth and immunity status.
Source: Journal of Mathematical Biology
Authors: Tom Britton, Andrea Pugliese
Institutions: Stockholm University, University of Trento
Language: English
Field: Medicine
Domain: Health Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Awards: G3141778957, G5225462043
OpenAlex ID: W4416199254