Pandemia de Influenza A(H1N1), México, 2009

Modeling the Geographical Spread of Influenza A(H1N1): The Case of Mexico
 

Rafael A Barrio, Carmen Varea, Tzipe Govezensky, Marco V José

Applied Mathematical Sciences 01/2013; 7(44):2143-2176.

ABSTRACT. In this paper we examine the mechanisms by which a given viral disease spreads successfully in a geographical region. We propose that the key factors that cause pandemics are of social nature, whose influence can be modeled by mobility parameters that take into account the different ways in which the disease can be transmitted. We use a new SEIR(S) model that is able to reproduce the temporal behavior of a given disease within a local homogeneous community. The geographical spread of the disease is studied by defining a two dimensional grid of cells, weighted by the population density, and a SEIR(S) model in each cell. The cells are coupled with their nearest neighbors, simulating terrestrial communications, and with long range links representing airline routes. We propose that the mechanisms of transmission depend on the length scale. We simulate other transportation events as thermal noise, which turns out to be a key factor. Numerical simulations are presented to illustrate the results of the model. Actual data on the population, communication networks and incidence of influenza pandemic in Mexico in 2009 are used to validate the model. The agreement with actual data is satisfactory. Furthermore, it accounts for the effect of social distancing measures implemented in Mexico during the 2144 Rafael A. Barrio et al. early stages of the pandemic. Since the model can predict the development of viral epidemics with few data from the early stages, it can be used to predict the effect of actions to be taken to reduce and mitigate the risks of pandemics.

I. Influenza incidence actual data.

II. Influenza incidence model simulation with intervention. 

III. Influenza incidence model simulation NO intervention.