An Outbreak Vector-host Epidemic Model with Spatial Structure: The 2015 Zika Outbreak in Rio de Janeiro

TL;DR

This paper develops a spatial epidemic model using partial differential equations to analyze the spread of Zika in Rio de Janeiro, providing insights into how spatial factors influence outbreak dynamics.

Contribution

It introduces a novel PDE-based spatial epidemic model specifically applied to the 2015 Zika outbreak in Rio de Janeiro, linking spatial parameters to epidemic outcomes.

Findings

Model is well-posed and mathematically sound.

Spatial parameters significantly affect epidemic spread.

Application to Zika outbreak demonstrates model's practical relevance.

Abstract

Background: A deterministic model is developed for the spatial spread of an epidemic disease in a geographical setting. The disease is borne by vectors to susceptible hosts through criss-cross dynamics. The model is focused on an epidemic outbreak that initiates from a small number of cases in a small sub-region of the geographical setting. Methods: Partial differential equations are formulated to describe the interaction of the model compartments. Results: The partial differential equations of the model are analyzed and proven to be well-posed. The epidemic outcomes of the model are correlated to the spatially dependent parameters and initial conditions of the model. Conclusions: A version of the model is applied to the 2015-2016 Zika outbreak in the Rio de Janeiro Municipality in Brazil.