Mathematical analysis of an age structured problem modeling phenotypic plasticity in mosquito behaviour

TL;DR

This paper provides a mathematical analysis of an age-structured model for mosquito phenotypic plasticity in blood-feeding behavior, exploring spectral properties and steady-state solutions.

Contribution

It introduces an analytical framework for understanding mosquito behavior plasticity using spectral analysis of an operator, advancing theoretical insights in vector biology modeling.

Findings

Spectral analysis of the operator $\\mathbb{A}$ reveals asymptotic behavior.

Conditions for existence and nonexistence of steady solutions are established.

The study enhances understanding of mosquito behavior dynamics in natural environments.

Abstract

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.