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| This paper proposes two modifiedsusceptible-infected-recovered-susceptible (SIRS) models onhomogenous and heterogeneous networks, respectively. In the study ofthe homogenous network model, it is proved that if the basicreproduction number $R_0$ of the model is less than one, then thedisease-free equilibrium is locally asymptotically stable andbecomes globally asymptotically stable under the condition that thethreshold value $R_1$ is less than one. Otherwise, if $R_0$ is morethan one, the endemic equilibrium is locally asymptotically stableand becomes globally asymptotically stable under the assume that thetotal population $N $ will tend to a specific plane. In the study ofthe heterogeneous network model, this paper discusses the existencesof the disease-free equilibrium and endemic equilibrium of themodel. It is proved that if the threshold value $ ilde{R}_0$ isless than one, then the disease-free equilibrium is globallyasymptotically stable. Otherwise, if $ ilde{R}_0$ is more than one,the system is permanent. A series of numerical experiments are givento illustrate the theoretical results. We also numerically predictthe effect of vaccination ratio on the size of HBV infected mainlandChinese population. |
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| Keywords:SIRS model; homogenous network; heterogeneous network; local stability; globalstability |
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