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Spatial spread of epidemic diseases in geographical settings: Seasonal influenza epidemics in Puerto Rico

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  • A deterministic model is developed for the spatial spread of an epidemic disease in a geographical setting. The model is focused on outbreaks that arise from a small number of infected individuals in sub-regions of the geographical setting. The goal is to understand how spatial heterogeneity influences the transmission dynamics of susceptible and infected populations. The model consists of a system of partial differential equations with a diffusion term describing the spatial spread of an underlying microbial infectious agent. The model is applied to simulate the spatial spread of the 2016-2017 seasonal influenza epidemic in Puerto Rico. In this simulation, the reported case data from the Puerto Rican Department of Health are used to implement a numerical finite element scheme for the model. The model simulation explains the geographical evolution of this epidemic in Puerto Rico, consistent with the reported case data.

    Mathematics Subject Classification: Primary: 35K55, 35B40, 92D30.


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  • Figure 1.  Top. The 76 municipalities in Puerto Rico (wikipedia.org). Bottom. The population density of Puerto Rico (wikipedia.org)

    Figure 2.  The population density of the initial susceptible population $ S_0({\bf x}) $

    Figure 3.  The geographical mesh with 552 nodes. In the simulations, 23772 nodes are used. The spatial units are kilometers

    Figure 4.  (top) Reported cases of seasonal influenza Puerto Rico in 2015-2016 (yellow graph) and 2016-2017 (black graph); (bottom) Total cases from the model simulation for 2016-2017

    Figure 5.  Estimated reported case data (per 100,000 inhabitants) for four municipalities Mayaqűez, Arecibo, San Juan, and Ponce in the 2016-2017 seasonal influenza epidemic in Puerto Rico. The epidemic arises in Mayaqűez, spreads to Arecibo and San Juan, and last to Ponce

    Figure 6.  Model simulation of total cases for four municipalities in the seasonal influenza 2016-2017 epidemic in Puerto Rico

    Figure 7.  Simulation of spatial spread of 2016-2017 influenza outbreak in Puerto Rico. The population density of Puerto Rico is set as the initial value of the susceptible population. The initial size of the infected population is assumed to be 30, concentrated in the northwest

    Figure 8.  Model simulation of the infected population densities (number of cases per 100,000 people) in the 2016-2017 seasonal influenza epidemic in Puerto Rico in all municipalities for weeks 4 (top left), 6 (top right), 10 (bottom left), and 18 (bottom right)

    Figure 9.  The total number of reported cases of influenza strain subtypes in 2015-2016. An outbreak of type B strain peaks at week 21 in 2016 (Departamento de Salud, Puerto Rico)

    Figure 10.  Estimated reported case data (per 100,000 inhabitants) from Departamento de Salud for four municipalities San Juan, Arecibo, Ponce, and Mayaqűez in the 2015-2016 seasonal influenza epidemic in Puerto Rico. The late second peak is present in all four municipalities

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