Media Coverage and Personal Protection Awareness with Hopf Bifurcation Analysis of Multi-Time Delay Vector-Borne Disease Model
Considering the effects of media coverage,personal protection awareness and time delays on the spread of vector-borne diseases,a model of vector-borne diseases with delayed media coverage and incubation period delays is developed.Firstly,the exact expression of the basic reproduction number is given and used to characterize the existence and stability of the equilibria and the existence of the Hopf bifurcation.That is,when the basic reproduction number is less than 1,the stability of disease-free equilibrium will not be affected by the media coverage delay and the latency delay of virus in vectors.When the basic reproduction number is greater than 1,the media coverage delay will affect the stability of the endemic equilibrium,and the model will generate the Hopf bifurcation.Further,by using the bifurcation theorem,the direction of Hopf bifurcation is discussed and some sufficient conditions for the stability of periodic solution are obtained.Finally,some numerical examples are given to explain the main theoretical results.
vector-borne diseasemedia coveragebasic reproduction numberHopf bifurcation and stability
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