@article{Liu2024, 
author = {Huihui Liu and Yaping Wang and Linfei Nie},
title = {Dynamical analysis and optimal control of an multi-age-structured vector-borne disease model with multiple transmission pathways},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {12},
pages = {36405-36443},
keywords = {vector-borne diseases, multiple routes of transmission, age structure, asymptomatic infection, optimal control},
url = {https://www.sciopen.com/article/10.3934/math.20241727},
doi = {10.3934/math.20241727},
abstract = {Based on the diversity of transmission routes and host heterogeneity of some infectious diseases, a dynamical model with multi-age-structured, asymptomatic infections, as well as horizontal and vectorial transmission, is proposed. First, the existence and uniqueness of the global positive solution of this model is discussed and the exact expression of the basic reproduction number  R0 is obtained using the linear approximation method. Further, we deduce that the disease-free steady state  E0 is globally asymptotically stable for  R0<1, the endemic steady state  E∗ exists and the disease is persistent for  R0>1. In addition, the locally asymptotically stability of  E∗ is also obtained under some certain conditions. Next, our model is extended to a control problem and the existence and uniqueness of the optimal control by using the Gateaux derivative. Finally, numerical simulations are used to explain the main theoretical results and discuss the impact of age-structured parameters and control strategies on the prevention and control of vector-borne infectious diseases.}
}