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

Abstract

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.

Pattern transitions in spatial epidemics: Mechanisms and emergent properties

“…For example, spatial patterns are indicative of the large scale trends of epidemics or of the rates of spread through space, which in turn may guide policy decisions. The types of patterns found in epidemiological studies include stationary patterns [38][39][40][41][42], wave patterns [43][44][45][46][47], patch invasion [48], and others [49][50][51][52].…”

Assessing the invasion speed of triatomine populations, chagas disease vectors evaluación de la velocidad de invasión de poblaciones de vectores triatominos de la enfermedad de chagas

“…Namely, for high enough vertical transmission (about 30% for our parameter estimates) hosts carry the wavefront, rather than vectors. It remains to develop more precise estimates of the processes under study in order to derive an estimate of invasion speed which can be compared with results of studies using other modeling approaches (e.g., [1]). These results will also permit the calculation and study of spatial as well as temporal variation in the infection's basic reproductive number, R 0 .…”

“…The mathematical model developed here uses integrodifference equations. To date the only other model developed to assess the invasion speed of sylvatic T. cruzi infection used a metapopulation model based on a large grid [1].…”

Stochastic Lattice gas Cellular Automata Model for Epidemics

“…In recent years the development of CA models for the spread of infectious diseases has increased. Both deterministic [16][17][18] and stochastic [19][20][21] designs have been developed.…”

“…In CA models for epidemics, each cell can be considered as an individual or a small subpopulation [22][23][24]. Alternatively, each cell may represent an area (patch) occupied by a certain number of individuals who can interact within the cell and move to other cells [17,19,25]. This will be the case in the model presented in this work.…”