一个描述血吸虫病的数学模型的周期解

研究一个描述血吸虫病的周期微分方程模型dx/dt=-rx+A/S(t)y,dy/dt=-δ(t)y+B(S(t)-y) x2/1+ x.数值计算发现该系统同时具有渐近稳定的零解和一个正周期解.通过证明该系统解的有界性,并在一个函数空间上构造单调有界序列,进而证明了在一定条件下正周期解的存在性.

On Periodic Solutions of a Mathematical Model on Schistosomiasis

A mathematical model on schistosomiasis governed by periodic differential equations dx/dt=-rx+A/S(t)y,dy/dt=-δ(t)y+B(S(t)-y)x2/1+x is studied in present paper.It follows from some numerical computations that there exists a positive periodic solution and zero solution,which is asymptotically stable.By discussion on boundedness of the solutions of this model,and construction of a monotonic sequence,the existence of positive periodic solution is proved.