Presence and infestation waves of hematophagous arthropod species

The invasion of hematophagous arthropod species in human settlements represents a threat, not only to the economy but also to the health system in general. Recent examples of this phenomenon were seen in Paris and Mexico City, evidencing the importance of understanding these dynamics. In this work, we present a reaction–diffusion model to describe the invasion dynamics of hematophagous arthropod species. The proposed model considers a denso-dependent growth rate and parameters related to the control of the invasive species. Our results illustrate the existence of two invasion levels (presence and infestation) within a region, depending on control parameter values. We also prove analytically the existence of the presence and infestation waves and show different theoretical types of invasion waves that result from varying control parameters. In addition, we present a condition threshold that determines whether or not an infestation occurs. Finally, we illustrate some results when considering the case of bedbugs and brown dog ticks as invasion species.