Abstract
ABSTRACTAn susceptible-infective-removed epidemic model incorporating media coverage with time delay is proposed. The stability of the disease-free equilibrium and endemic equilibrium is studied. And then, the conditions which guarantee the existence of local Hopf bifurcation are given. Furthermore, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. The obtained results show that the time delay in media coverage can not affect the stability of the disease-free equilibrium when the basic reproduction number is less than unity. However, the time delay affects the stability of the endemic equilibrium and produces limit cycle oscillations while the basic reproduction number is greater than unity. Finally, some examples for numerical simulations are included to support the theoretical prediction.
Highlights
Epidemic models with time delays have received much attention since time delays can change the qualitative behaviour of the models
In the sense of infectious diseases, we conclude that the time delay in media coverage cannot influence the stability of the disease-free equilibrium when R0 < 1
We proposed an SIR epidemic model incorporating media coverage with time delay
Summary
Epidemic models with time delays have received much attention since time delays can change the qualitative behaviour of the models It can change the stability of equilibrium and lead to periodic solutions by Hopf bifurcation [6,10,11,12,14,17,18,21,27,28,29,30]. The study shows that students from Ontario, Canada were aware that the risk of becoming infected by the SARS coronavirus was low, but they predominantly had misconceptions about the virus It is important for public health authorities to communicate accurate and timely information to the public about infectious disease outbreaks. Based on the above assumption, we propose an susceptible-infective-removed (SIR) epidemic model incorporating media coverage with time delay which can be described as follows: dS(t) = dt β2I(t − τ ) m + I(t − τ.
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