Effect of Concurrent Partnerships and Sex-Act Rate on Gonorrhea Prevalence

The disease gonorrhea (GC) is a major public health problem in the United States, and the dynamics of the spread of GC through popula tions are complicated and not well understood. Studies have drawn attention to the effect of concurrent sexual partnerships as an influen tial factor for determining disease prevalence. However, little has been done to date to quantify the combined effects of concurrency and within-partnership sex-act rates on the prevalence of GC. This simulation study examines this issue with a simplified model of GC transmission in closed human populations that include concurrent partnerships. Two models of within-partnership sex-act rate are compared; one is a fixed sex-act rate per partnership, and the other is perhaps more realistic in that the rate depends on the number of concurrent partners. After controlling for total number of sex acts, pseudo-equilibrium prevalence is higher with the fixed sex-act rate than under the concurrency-adjusted rate in all the modeled partnership formation conditions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68414/2/10.1177_003754979807100404.pd

Global analysis of a Holling type II predator–prey model with a constant prey refuge

A global analysis of a Holling type II predator–prey model with a constant prey refuge is presented. Although this model has been much studied, the threshold condition for the global stability of the unique interior equilibrium and the uniqueness of its limit cycle have not been obtained to date, so far as we are aware. Here we provide a global qualitative analysis to determine the global dynamics of the model. In particular, a combination of the Bendixson–Dulac theorem and the Lyapunov function method was employed to judge the global stability of the equilibrium. The uniqueness theorem of a limit cycle for the Lineard system was used to show the existence and uniqueness of the limit cycle of the model. Further, the effects of prey refuges and parameter space on the threshold condition are discussed in the light of sensitivity analyses. Additional interesting topics based on the discontinuous (or Filippov) Gause predator–prey model are addressed in the discussion