Invasion Speed in Cellular Automaton Models for T. cruzi Vector Migration

The parasite Trypanosoma cruzi, known for causing Chagas’ disease, is spread via insect vectors from the triatomine family. T. cruzi is maintained in sylvatic vector-host transmission cycles in certain parts of the Americas. Communication between the cycles occurs mainly through movement (migration) of the insect vectors. In this study, we develop a cellular automaton (CA) model in order to study invasion of a hypothetical strain of T. cruzi through the region defined by the primary sylvatic cycles in northern Mexico and parts of the southeastern United States. The model given is a deterministic CA, which can be described as a large metapopulation model in the format of a dynamical system with 9,376 equations. The migration rates in the model, used as coupling parameters between cells in the CA, are estimated by summing up the proportion of vectors crossing patch boundaries (i.e., crossing from one cell to another). Specifically, we develop methods for estimating speed and direction of invasion as a function of vector migration rates, including preference for a particular direction of migration. We develop two methods for estimating invasion speed: via orthogonal local velocity components and by direct computation of magnitude and direction of an overall velocity vector given a front created by cells identified as being invaded by the epidemic. Results indicate that invasion speed is greatly affected by both the physical and the epidemiological landscapes through which the infection wave passes. A power-law fit suggests that invasion speed increases at slightly less than the square root of increases in migration rate.