Research On Infectious Disease Model Based On Information Dissemination

With the extensive development of mass media, the efect of awareness programs onthe disease is obvious. In this paper, in order to make the model realistic we construct twotypes of infectious disease model with delay and analyze the model by using stability theoryof diferential equations.It is assumed that pathogens are transmitted via direct contact between the susceptibleand infective, and further assumed that the growth rate of cumulative density of awarenessprograms increases at a rate proportional to the infective. An epidemic model with timedelay has been proposed and analyzed to the efect of awareness programs driven by mediaon the prevalence of an infectious disease. We analyze the model by using stability theoryof diferential equations and the system exhibits two equilibria: if the basic reproductionnumber R0<1the disease-free equilibrium is stable, which is unstable when R0>1andnow the unique endemic equilibrium occurs. The time delay τ has no efect on the stabilityof equilibria. Numerical simulations suggest the results we obtained and the increasing of thedissemination rate λ and implementation rate μ can reduce the proportion of the infectivepopulation.We hold the opinion that awareness programs can infuence the susceptible to a limitedextent for some objective factors, consider that the cumulative density of awareness programsat time t being executed will be in accordance with the infected cases reported at timet τ(τ>0), then give and discuss a compartment epidemic model with delay. The systemexhibits two equilibria: the disease-free equilibrium is stable if the basic reproduction numberR0>1, and when R0>1, τ <τ0, the unique endemic equilibrium occurs Hopf-bifurcation.Numerical simulations prove the stability of equilibria and τ0=30.12, then if we want toreduce the proportion of the infective population, we can increase of the dissemination rateλ and implementation rate μ. Finally we prove the existence of τ.People comprehend the disease through awareness programs and take relevant measuresto reduce the possibility of being infected，in short media is a key tool for infuencing people behavior towards the disease to devise proper policies for controlling the epidemic.