Analysis And Research On Vector-borne Disease Model With Impulsive Control

Vector-borne disease has caused worldwide public concern due to its threaten to human health.Impulsive control management is proved to be effective on preventing vectors,which makes it imperative to construct and investigate epidemic models for vector-borne disease with impulsive intervention.In this dissertation,based on the transmission mechanism and implementation of practical control strategies,we formulate and study several epidemic models for vector-borne disease that incorporate impulsive control techniques.The contents are as follows:According to the spread of malaria,an impulsive model with standard incidence and re-infection is formulated and analyzed theoretically and numerically in terms of impulse at fixed times and state-dependent impulse.The results reveal that the dynamical behaviors of the model are determined by the threshold R₀.When R₀（27）1,there exists a disease-free periodic solution that is locally stable,otherwise the disease is uniformly persistent ifR₀（29）1.Furthermore,when impulsive intensity is taken as the bifurcation parameter,nontrivial periodic solution can be bifurcated at ₀R（28）1.In addition to simulations of parameter sensitivity,the efficiency of state-dependent control is also conducted numerically.In consideration of impulsive control for the vectors and saturation treatment for infected hosts,an SIR-SI model for vector-borne disease is proposed and investigated.The influence of impulsive period and impulsive intensity as well as saturation treatment is analyzed.By the theory of impulsive differential equation and comparison theorem,the existence and stability of disease-free periodic solution is discussed and uniform persistence of the disease is proved when the threshold is greater than one.Numerical simulations,including numerical solutions of the model and bifurcation diagrams,are conducted with respect to impulsive period,impulsive intensity and varying treatment,showing rich dynamics of the system such as bifurcation and chaos.An SIR-SI impulsive differential model for vector-borne disease with bilinear incidence is established and studied.The threshold R₀ that determines the dynamics the model is defined.By the theory of Floquet operator and comparison theorem,the results indicate that there exists a disease-free periodic solution which is globally asymptotically stable if the threshold is less than one.Otherwise,it is proved that the disease is uniformly persistent when the threshold is greater than one.In case of R₀（27）1 and ₀R（29）1,numerical solutions of the model are simulated respectively.In addition,for the state-dependent control management,the influence of impulsive intensity and critical threshold on impulsive control implementation is examined.