Dynamics Of An Almost Periodic Dengue Fever Model With Age Structure And Time-delayed In A Patchy Environment

Dengue fever is an vector disease transmitted by mosquito’s bite.Its spread and prevalence are affected and restricted by many factors.Because newborns can inherit strong immunity from their mothers and be immunized with timely vac-cines,then avoiding the invasion of disease,and only adult mosquitoes are involved in the spread of disease,which leads to the age structure and time-delayed playing a very important role in the spread of diseases.In addition,seasonality is also a major factor affecting the spread of disease,it is often reflected by periodicity,whereas almost periodic functions as a generalization of periodic functions,which can comprehensively describe the role of seasonality in disease transmission.This paper mainly uses the monotone dynamical system,nonlinear functional theory,skew-product semiflow to study the dynamics of an almost periodic dengue fever model with age structure and time-delayed.Firstly,under some reasonable assumptions,an almost periodic dengue SIR-SEI model with age structure and time-delayed is deduced;secondly,for this model,existence of disease-free almost periodic solution is proved,and the basic reproduction number₀of dengue model is defined according to the next gen-eration regeneration operator;next,it is concluded that the basic reproduction number₀is the important threshold parameter for judging the extinct or per-sistence of disease,that is,when₀>1,the model has a positive almost periodic solution,the disease is uniformly persistent;when₀<1,and the susceptible,the infective and the recovered host population have the same travel rate and a small invasion in different patches,the disease-free almost periodic solution is global-ly stable,the disease is extinct.Finally,we consider two patches.In this case,numerical simulation is used to to verify the theoretical results and gives mea-sures to control the spread of disease.For example,by reducing the bite rate of mosquitoes,or limiting travel rate of between patches to control spread of disease.