This paper presents an age structured problem modelling mosquito blood-feeding plasticity in a natural environment. We first investigate the analytical asymptotic solution through studying the spectrum of an operator $\mathbb{ A}$ which is the infinitesimal generator of a $C_0$-semigroup. Indeed, the study of the spectrum of $\mathbb{ A}$ { \it per se} is interesting. Additionally, we get the existence and nonexistence of nonnegative steady solutions under some conditions.
Categories: math.AP