Role of media coverage and delay in controlling infectious diseases: A mathematical model

摘要

The aim of this paper is to investigate the effect of awareness coverage and delay in controlling infectious diseases. We formulate an SIS model considering individuals’ behavioral changes due to the influences of media coverage and divide the susceptible class into two subclasses: aware susceptible and unaware susceptible. Other model variables are infected human and media campaign. It is assumed that the rate of becoming aware (unaware), from unaware to aware susceptible human (from aware to unaware susceptible human), is a function of media campaign. A time delay is considered for the time that is taken by an unaware (aware) susceptible individual to become aware (unaware). An additional time delay is considered due to the time lag needed in organising awareness campaigns. The model exhibits two equilibria: the disease-free equilibrium and the endemic equilibrium. The disease-free equilibrium is stable if the basic reproduction number is smaller than unity and the endemic equilibrium exhibits a Hopf-bifurcation, in both delayed and non-delayed system, whenever it exists. Analytical and numerical results prove the significance of awareness and delay on the prevalence of infectious diseases.