  To understand how impulsive intervention and regional evolution jointly
influence the spread of faecal-oral diseases, this paper develops an impulsive
faecal-oral model in a periodically evolving environment. The well-posedness of
the model is first checked. Then, the existence of the principal eigenvalue
dependent on impulse intensity and evolving rate is proved based on
Krein-Rutman theorem. With the help of this value, the threshold dynamical
behaviours of the model are explored. More importantly, this paper also derives
the monotonicity of the principal eigenvalue with respect to initial region and
impulse intensity and estimates the principal eigenvalue in some special cases.
Finally, numerical simulations are used to verify the correctness of the
theoretical results and to explore the impact of regional evolution rate on the
spread of the diseases. Our research shows that large impulsive intensity
$1-g'(0)$ and small evolving rate $\rho(t)$ play a positive role in the
prevention and control of the diseases.
