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Differential equation models of some parasitic infections: Methods for the study of asymptotic behavior. (English) Zbl 0637.92008

Consider the two-dimensional system of ODEs arising in the study of transmission of parasitic infections:

(s)w ' =-μ 1 w-μ 1 T 1 y,y ' =-μ 2 y+μ 2 T 2 ϕ(w)(1-y),

with initial conditions w(0)0, and 0y(0)1. Here μ 1 , μ 2 , T 1 , T 2 are positive constants and the function ϕ, which represents the expected number of ovipositing worms per vertebrate host, depends on the sexuality of the parasite.

The authors regard ϕ 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.

Reviewer: Li.Bingxi
MSC:
92D25Population dynamics (general)
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
34E99Asymptotic theory of ODE
34C99Qualitative theory of solutions of ODE