Threshold Dynamics Of Almost Periodic Malaria Transmission Models

The continuous globalization trend of infectious diseases reflects the importance of the prevention and control strategy of infectious diseases.The outbreak of the infectious disease due to complicated effect of many factors,including temporal and spatial heterogeneity,which are important factors on disease transmission.Spatial heterogeneity is modeled by using the multi-patch framework and assuming that individuals travel among different patches,temporal heterogeneity is caused by sea-sonal factors,which are often reflected by periodicity.As a generalization of periodic functions,almost periodic functions represent accurately the impact of the season-ality in the spread of infectious disease.We study the dynamics of almost periodic Malaria transmission model by mean-s of(monotone)dynamical system,nonlinear functional analysis,and establish the theory of the basic reproduction ratio and its computation formulae with assumption that the time dependent parameters are almost periodic.Furthermore,we also apply the developed theory to obtain a threshold type result for uniform persistence and global extinction of the disease.Combining with the birth rate and other factors,we will consider the basic reproduction number of malaria transmission model,and the global asymptotic behavior of almost periodic solution in order to provide a policy for the prevention and control of a disease.Finally we has carried on the numerical simulations,concentrating on confirming the feasibility and rationality of theoretical research in practical world,in the meantime data analysis give an information about the effect of travel control on disease transmission.