Modeling and optimal control of the spread of invasive species in heterogeneous landscapes using cellular automata

Abstract

This study deals with the phenomenon of propagation of invasive species that generate ecological, environmental and economic problems on a large scale. There are different models that address this type of phenomenon to establish optimal policies and strategies that can eradicate or control outbreaks of invasive species. Most models are based in space-time, however, they do not usually take into account the heterogeneity of the landscape in which there are spatial characteristics that naturally govern the dynamics of the outbreaks in combination with other variables related to the behavior of the invasive species and victim species. This paper proposes an economic model that determines the optimal policies for control of an outbreak; the model captures information related to the heterogeneity of the space considering some of the spatial characteristics of the landscape that have an incidence in the phenomenon, in order to have a better prediction regarding the dynamics of the outbreaks. The model consists of a dynamic optimization problem based on cellular automata, therefore, in addition to determining the optimal control strategies, it also allows us to visualize the dynamics of the phenomenon in each projected time. The model was applied to different landscape heterogeneity scenarios and contrasted with homogeneous landscapes, obtaining interesting results that confirm the importance of heterogeneity in invasive species models.