Modelling by Generation of Poisson Distributed Numbers of First Historical Zika Outbreak in Salta, Argentina

Aims/ Objectives:: In this work we describe the first historical Zika virus outbreak recorded in Salta, Argentina, in the year 2017, through Monte Carlo-type simulations using the Poisson model. Later we made comparisons with previous results.Study Design: Retrospective-descriptive studies and stochastic computational experiment analysis Place and Duration of Study: Department of Mathematic, Faculty of Exact Sciences. National University of Salta, Argentina, from March 2021 to December 2023.Methodology: Descriptive and computational experiment analysis. Parameter estimation by Maximum Likelihood and Simulation of type Monte Carlo.Results: We describe the probabilistic behavior through Monte Carlo simulations of the first historical outbreak of Zika in Salta Argentina, 2017. Based on the data of registered Zika cases, we estimate a probabilistic Poisson model with parameter\(\hat{\lambda}\) = 13:092 casesweek-1 and confidence interval 95%CI [11:889- 15:110]. Finally, by computational experiments we generate epidemic outbreaks with 20 runs. The computational experiments shows that, from a qualitative point of view, the descriptions of the outbreak are qualitatively acceptable and they were not better than the probabilistic model obtained in a previous study. However, from the statistical point of view, carrying out computational experiments of 10 comparative runs in each model, the models provide simulations of epidemic outbreaks by Zika virus, for this region of Salta, Argentina, that do not differ significantly at a confidence level of 5%.