Global stability of an SIRS epidemic model with transport-related infection

An SIRS model is proposed to study the effect of transport-related infection. Some analytical results are given for an SIRS model. If the basic reproduction number R0γ ⩽ 1, there only exists the disease-free equilibrium which is globally asymptotically stable. There exists an endemic equilibrium which is locally asymptotically stable if the basic reproduction number R0γ > 1. Sufficient conditions are established for global asymptotic stability of the endemic equilibrium. It is shown that the disease is endemic in the sense of permanence if and only if the endemic equilibrium exists. This implies that transport-related infection on disease can make the disease endemic even if all the isolated regions are disease free.