Modelling spatial-time dynamics of dengue epidemics in urban centers: comparison with epidemics time-series in Salvador-Brazil
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Dengue is a vector-borne infectious disease with a very complex dynamics, occurring mainly in urban centers. According to WHO, around 80 millions people become infected each year in all continents around the world, except Europe. In Brazil, where only three of four serotypes were isolated so far, dengue epidemics have occurred in many urban centers since the eighties.
Some continuous mathematical models for dengue have been developed, but most of them do not take into account the spatial distribution of humans and mosquitoes. In this work we propose and analyze a probabilistic two-dimensional cellular automata model, and its mean-field version (differential equations), that is able to describe the dynamics of dengue epidemics in urban centers and to evaluate the impact of vector control actions on dengue occurrence. In this model, we consider three connected lattices of humans, vectors and no-winged phase of the vectors, taking into account the seasonality effects (pluviometric data), the mobility of humans and the possibility of vector control. The cellular automata model is able to reproduce the time-series of the first dengue epidemic in Salvador, an urban center in the Northeast region of Brazil, in 1995. It shows the fluctuations that are not captured by its mean-field version. It also provides qualitatively the spatial-time patterns of the epidemics visualized in real-time using the graphical library g2. The stationary states of the mean-field version give a suitable approach to analyze the vector control measures.
Based on the study of parameter space of the discrete model and on the stationary states of the mean-field version, we observe: i) the changes of behavior occur for the range of the suitable parameter values indicated in the literature; ii) concerning the control strategies, besides the use of both adulticide and larvacide to control the vector, it is extremely relevant to remove the existent vector breeding sites and to avoid the emergence of new ones. Aiming to exam dengue epidemics in different urban centers, we implemented a routine of parameter optimization that is able to display the most probable values of some parameters involved in the dengue dynamics, comparing with actual time-series. Finally, motivated by the mobility of humans in urban centers during the day when the mosquitoes bite the humans, we are generalizing our cellular automata model to a model on complex networks with no local interactions.