-
Abstract
In this study, we expand on the susceptible-infected-susceptible
(SIS) heterosexual mixing setting by including the movement of
individuals of both genders in a spatial domain in order to more
comprehensively address the transmission dynamics of competing
strains of sexually-transmitted pathogens. In prior models, these
transmission dynamics have only been studied in the context of
nonexplicitly mobile heterosexually active populations at the
demographic steady state, or, explicitly in the simplest context
of SIS frameworks whose limiting systems are order preserving.
We introduce reaction-diffusion equations to study the dynamics of
sexually-transmitted diseases (STDs) in spatially mobile
heterosexually active populations. To accomplish this, we study a
single-strain STD model, and discuss in what forms and at what
speed the disease spreads to noninfected regions as it expands its
spatial range. The dynamics of two competing distinct strains of
the same pathogen on this population are then considered. The
focus is on the investigation of
the spatial
transition dynamics between the two endemic equilibria supported
by the nonspatial corresponding model. We establish conditions for
the successful invasion of a population living in endemic
conditions by introducing a strain with higher fitness. It is
shown that there exists a unique spreading speed (where the
spreading speed is characterized as the slowest speed of a class
of traveling waves connecting two endemic equilibria) at which the
infectious population carrying the invading stronger strain
spreads into the space where an equilibrium distribution has been
established by the population with the weaker strain. Finally, we
give sufficient conditions under which an explicit formula for the
spreading speed can be found.
Mathematics Subject Classification: Primary: 92D40, 92D25; Secondary: 35K55, 35K57.
\begin{equation} \\ \end{equation}
-
Access History
-