DOI: 10.5061/dryad.hmgqnk9rr
title: A stochastic framework for predicting epidemiological risk areas using the Ornstein-Uhlenbeck process: Software and supplementary material

description: 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.
description: All the data used to obtain the results are uploaded. The scripts
 were developed in Python language. Figures generated from the scripts in
 Python. A zip file with all the scripts is also
 included.
description: # A stochastic framework for predicting epidemiological risk areas using
 the Ornstein-Uhlenbeck process: Software and supplementary material
 [https://doi.org/10.5061/dryad.hmgqnk9rr](https://doi.org/10.5061/dryad.hmgqnk9rr) ## Description of the data and file structure The scripts that generate the figures in the article are described in Phyton. Each case and variables are described in the related executable code (see Code/Software below). ## Sharing/Access information Don't apply. ## Code/Software The executables are in Python language and described as follows: 1. Run the file figure1_article.py to generate the results of Figure 1 (see figure "aedes.pdf" *). 2. Run the file figure2_article.py to generate the results of Figure 2 (see "mosquitos 1.pdf" *). 3. Run the file figure3_article.py to generate the results of Figure 3 (see "mosquitos 2.pdf" *). 4. Run the file figure4_article.py to generate the results of Figure 4 (see "mosquitos 3.pdf" *). 5. Run the file R_0.py to generate the basic reproduction number. ## **General description of variables** Variables used on the computational scripts: **betta** - Infection rate (week^-1) **gamma** - Human recovery rate   (week^-1) **eta** - Infectiousness decay rate  (week^-1) **bm** - Mosquito mortality rate (10% daily)  (week^-1) **m** - Proportion of mosquito Nv/nh (adimensional) **tA** - Asymptomatic transmission period (week-1) **RAh** - Basic reproduction number related to host-vector (R_0A)  (adimensional) **R_eta** - Basic reproduction number related to host-vector (R_0S)  (adimensional) **Rm** - Basic reproduction number related to vector-host (R_0^v)  (adimensional) **R0** - Basic reproduction number  (adimensional) **mu** - mortality rate  (week^-1) **Ng** - Number time generation  (adimensional) **tg** - Generation time (week) **iip** - Intrinsic incubation period  (week^-1) **eip** - Extrinsic incubation period  (week^-1) **b** - removal rate  (week^-1) **t** - Ng * Tg - time (week) **L** - Diffusion lenght (km - kilometer) **N** - number of partitions (plot parameters) **p** - number of isolines  (plot parameters) **k** - t max  (week) *Figures are included in the manuscript  and generated with Python.  **Version 13.01.2025:** ** **Small corrections on the scripts. Addition of 2 scripts from new analysis. Change of the title and abstract of the article following the reviewers' suggestion.