A stochastic framework for predicting epidemiological risk areas using the Ornstein-Uhlenbeck process: Software and supplementary material

Understanding the spatiotemporal distribution of infection risk is
fundamental in the epidemiology of infectious diseases, as it allows for
the identification of key parameters influencing disease transmission.
Insights into the spatiotemporal drivers of epidemic dynamics are
essential for developing improved strategies for disease prevention. This
study introduces a predictive framework based on the Ornstein-Uhlenbeck
stochastic process to estimate the spatial and temporal distribution of
infectiousness originating from a primary case. The proposed model
captures the dynamics of secondary infections and their impact on spatial
dispersion, primarily driven by a diffusion mechanism of the Chapman type.
This diffusion mechanism induces the phenomenon of segregation by
incorporating behavioral or cognitive aspects of susceptible individuals.
We calculate critical epidemiological metrics, including the basic
reproduction number, the probability density function of generation time,
and the mean generation time. Notably, the model reveals that 38.5% of
dengue infections occur before the onset of symptoms, highlighting the
critical need to address presymptomatic transmission in control
strategies. This silent dissemination increases the complexity of the
objective of the model presented, which seeks to answer the fundamental
public health question of when the pathogen will reach a specific region.
The proposed mathematical model establishes a framework for selecting
emerging risk areas, prioritizing interventions and optimizing resource
allocation.