A discrete-time mathematical model of stage-structured mosquito populations

Abstract

This paper proposes a system of difference equations to model mosquito population. In this study, we develop and analyze the stage-structured models which consist of four distinct mosquito metamorphic stages: eggs, larvae, pupae, and adults. First, a model with constant birth rate is studied, and the inherent net reproduction number ℜ of the model is derived. If ℜ < 1 , the extinction equilibrium is globally asymptotically stable. If ℜ > 1 , there exists a unique positive equilibrium which is uniformly persistent. When breeding is seasonal for a special case, it indicates that a unique globally asymptotically stable periodic solution is admitted when the net reproductive number is larger than one. When this value is less than one, the mosquito population goes to extinction. Finally, numerical simulations to demonstrate our findings and brief discussion are also provided.