Spatial spread of sexually transmitted diseases within susceptible populations at demographic steady state - Carlos Castillo-Chavez; Bingtuan Li (Mathematical Biosciences and Engineering)
In this study, we expand on the susceptible-infected-susceptible(SIS) heterosexual mixing setting by including the movement ofindividuals of both genders in a spatial domain in order to morecomprehensively address the transmission dynamics of competingstrains of sexually-transmitted pathogens. In prior models, thesetransmission dynamics have only been studied in the context ofnonexplicitly mobile heterosexually active populations at thedemographic steady state, or, explicitly in the simplest contextof SIS frameworks whose limiting systems are order preserving.We introduce reaction-diffusion equations to study the dynamics ofsexually-transmitted diseases (STDs) in spatially mobileheterosexually active populations. To accomplish this, we study asingle-strain STD model, and discuss in what forms and at whatspeed the disease spreads to noninfected regions as it expands itsspatial range. The dynamics of two competing distinct strains ofthe same pathogen on this population are then considered. Thefocus is on the investigation of the spatialtransition dynamics between the two endemic equilibria supportedby the nonspatial corresponding model. We establish conditions forthe successful invasion of a population living in endemicconditions by introducing a strain with higher fitness. It isshown that there exists a unique spreading speed (where thespreading speed is characterized as the slowest speed of a classof traveling waves connecting two endemic equilibria) at which theinfectious population carrying the invading stronger strainspreads into the space where an equilibrium distribution has beenestablished by the population with the weaker strain. Finally, wegive sufficient conditions under which an explicit formula for thespreading speed can be found.