| dc.description.abstract | Background
Forecasting influenza outbreaks remains a significant challenge due to the complexity of dis
ease transmission and the influence of environmental and behavioral factors. Traditional
models based solely on the basic reproduction number (R0) often fall short in capturing the
full scope of outbreak dynamics.
Methods
In this study, we employ a seasonally adjusted SEIRT model incorporating stochastic differ
ential equations (SDEs), including Brownian motion and L´evy jump processes, to simulate
random and abrupt fluctuations in transmission. A branching process approximation is used
to evaluate the probability of an epidemic under the influence of seasonal variability and
stochastic perturbations. The model is calibrated using weekly influenza case data from
Mexico, with noise components estimated from publicly available CDC [1] and WHO [2]
surveillance data.
Results
Simulation results show that the inclusion of stochastic effects and periodic transmission
rates significantly enhances the model’s accuracy in reflecting real-world epidemic dynamics.
Numerical comparisons between deterministic, Brownian-based, and L´evy-based scenarios
reveal that both the initial state of the exposed or infectious subpopulation and the seasonal
transmission patterns are critical to determining outbreak probabilities. Results indicate that
seasonal transmission rates and stochastic effects significantly alter epidemic probabilities,
with L´evy processes capturing abrupt outbreak dynamics more accurately than deterministic
models.
Conclusions
The findings underscore that deterministic models may underestimate epidemic risk when
they overlook random and sudden changes in contact rates or disease introduction. The
proposed stochastic modeling framework yields a deeper understanding of influenza transmis
sion dynamics by incorporating uncertainty and seasonal variability, thereby supporting more
informed and effective public health decision-making. | en_US |
