Table 3.1.

Stationary solutions for System (2.8), and their characteristics

Stationary point	Location	Bifurcation conditions	Local stability condition
Liver-free	(0,0)	r = d	Never stable
Disease-free	(1,0)	b = d	b < d
Total-infection	(0, 1 − d/r)	r = d + d/b, r = d	r > d + d/b
Partial-infection	$\left(\frac{\text{db}+\text{d}-\text{br}}{\text{b}(1+\text{b}-\text{r})},\frac{\text{b}-\text{d}}{\text{b}(1+\text{b}-\text{r})}\right)$	r = d + d/b, b = d	rb/(1 +b) < d < b