Consider the two-dimensional system of ODEs arising in the study of transmission of parasitic infections:
with initial conditions w(0), and . Here , , , are positive constants and the function , which represents the expected number of ovipositing worms per vertebrate host, depends on the sexuality of the parasite.
The authors regard as an arbitrary function subject only to mild regularity conditions and study solutions of the initial value problem for (s). They discovered three new methods of establishing asymptotic behavior.
Contents: 1. Introduction; 2. The problem of global existence; 3. The method of the energy integral; 4. A generalized l’Hospital rule and the method of fluctuations, 5. The Sturm comparison method.